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<title>LaTeX syntax for mathematics</title>
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<main id="latex-syntax-for-mathematics">
<h1 class="title">LaTeX syntax for mathematics</h1>

<div class="topic abstract" role="doc-abstract">
<p class="topic-title">Abstract</p>
<p>Docutils supports mathematical content with a <a class="reference external" href="https://docutils.sourceforge.io/docs/ref/rst/directives.html#math">&quot;math&quot;
directive</a> and <a class="reference external" href="https://docutils.sourceforge.io/docs/ref/rst/roles.html#math">role</a>. The input format is <em>LaTeX math
syntax</em><a class="brackets" href="#math-syntax" id="footnote-reference-1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> with support for literal Unicode symbols.</p>
</div>
<!-- Minimal menu bar for inclusion in documentation sources
in ``docutils/docs/*/`` sub-sub-diretories.

Attention: this is not a standalone document. -->
<nav class="contents" id="contents" role="doc-toc">
<p class="topic-title">Contents</p>
<ul class="auto-toc simple">
<li><p><a class="reference internal" href="#inline-formulas-and-displayed-equations" id="toc-entry-1"><span class="sectnum">1 </span>Inline formulas and displayed equations</a></p></li>
<li><p><a class="reference internal" href="#mathematical-symbols" id="toc-entry-2"><span class="sectnum">2 </span>Mathematical symbols</a></p>
<ul class="auto-toc">
<li><p><a class="reference internal" href="#accents-and-embellishments" id="toc-entry-3"><span class="sectnum">2.1 </span>Accents and embellishments</a></p></li>
<li><p><a class="reference internal" href="#binary-operators" id="toc-entry-4"><span class="sectnum">2.2 </span>Binary operators</a></p></li>
<li><p><a class="reference internal" href="#extensible-delimiters" id="toc-entry-5"><span class="sectnum">2.3 </span>Extensible delimiters</a></p>
<ul class="auto-toc">
<li><p><a class="reference internal" href="#pairing-delimiters" id="toc-entry-6"><span class="sectnum">2.3.1 </span>Pairing delimiters</a></p></li>
<li><p><a class="reference internal" href="#nonpairing-delimiters" id="toc-entry-7"><span class="sectnum">2.3.2 </span>Nonpairing delimiters</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#extensible-vertical-arrows" id="toc-entry-8"><span class="sectnum">2.4 </span>Extensible vertical arrows</a></p></li>
<li><p><a class="reference internal" href="#functions-named-operators" id="toc-entry-9"><span class="sectnum">2.5 </span>Functions (named operators)</a></p></li>
<li><p><a class="reference internal" href="#greek-letters" id="toc-entry-10"><span class="sectnum">2.6 </span>Greek letters</a></p></li>
<li><p><a class="reference internal" href="#letterlike-symbols" id="toc-entry-11"><span class="sectnum">2.7 </span>Letterlike symbols</a></p></li>
<li><p><a class="reference internal" href="#math-alphabets" id="toc-entry-12"><span class="sectnum">2.8 </span>Math alphabets</a></p></li>
<li><p><a class="reference internal" href="#miscellaneous-symbols" id="toc-entry-13"><span class="sectnum">2.9 </span>Miscellaneous symbols</a></p></li>
<li><p><a class="reference internal" href="#punctuation" id="toc-entry-14"><span class="sectnum">2.10 </span>Punctuation</a></p></li>
<li><p><a class="reference internal" href="#relation-symbols" id="toc-entry-15"><span class="sectnum">2.11 </span>Relation symbols</a></p>
<ul class="auto-toc">
<li><p><a class="reference internal" href="#arrows" id="toc-entry-16"><span class="sectnum">2.11.1 </span>Arrows</a></p></li>
<li><p><a class="reference internal" href="#comparison" id="toc-entry-17"><span class="sectnum">2.11.2 </span>Comparison</a></p></li>
<li><p><a class="reference internal" href="#miscellaneous-relations" id="toc-entry-18"><span class="sectnum">2.11.3 </span>Miscellaneous relations</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#variable-sized-operators" id="toc-entry-19"><span class="sectnum">2.12 </span>Variable-sized operators</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#notations" id="toc-entry-20"><span class="sectnum">3 </span>Notations</a></p>
<ul class="auto-toc">
<li><p><a class="reference internal" href="#top-and-bottom-embellishments" id="toc-entry-21"><span class="sectnum">3.1 </span>Top and bottom embellishments</a></p></li>
<li><p><a class="reference internal" href="#extensible-arrows" id="toc-entry-22"><span class="sectnum">3.2 </span>Extensible arrows</a></p></li>
<li><p><a class="reference internal" href="#affixing-symbols-to-other-symbols" id="toc-entry-23"><span class="sectnum">3.3 </span>Affixing symbols to other symbols</a></p></li>
<li><p><a class="reference internal" href="#matrices" id="toc-entry-24"><span class="sectnum">3.4 </span>Matrices</a></p></li>
<li><p><a class="reference internal" href="#spacing-commands" id="toc-entry-25"><span class="sectnum">3.5 </span>Spacing commands</a></p></li>
<li><p><a class="reference internal" href="#modular-arithmetic-and-modulo-operation" id="toc-entry-26"><span class="sectnum">3.6 </span>Modular arithmetic and modulo operation</a></p></li>
<li><p><a class="reference internal" href="#roots" id="toc-entry-27"><span class="sectnum">3.7 </span>Roots</a></p></li>
<li><p><a class="reference internal" href="#boxed-formulas" id="toc-entry-28"><span class="sectnum">3.8 </span>Boxed formulas</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#fractions-and-related-constructions" id="toc-entry-29"><span class="sectnum">4 </span>Fractions and related constructions</a></p></li>
<li><p><a class="reference internal" href="#delimiter-sizes" id="toc-entry-30"><span class="sectnum">5 </span>Delimiter sizes</a></p></li>
<li><p><a class="reference internal" href="#text" id="toc-entry-31"><span class="sectnum">6 </span>Text</a></p></li>
<li><p><a class="reference internal" href="#integrals-and-sums" id="toc-entry-32"><span class="sectnum">7 </span>Integrals and sums</a></p>
<ul class="auto-toc">
<li><p><a class="reference internal" href="#altering-the-placement-of-limits" id="toc-entry-33"><span class="sectnum">7.1 </span>Altering the placement of limits</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#changing-the-size-of-elements-in-a-formula" id="toc-entry-34"><span class="sectnum">8 </span>Changing the size of elements in a formula</a></p></li>
</ul>
</nav>
<section id="inline-formulas-and-displayed-equations">
<h2><a class="toc-backref" href="#toc-entry-1" role="doc-backlink"><span class="sectnum">1 </span>Inline formulas and displayed equations</a></h2>
<p>The <strong>math role</strong> can be used for inline mathematical expressions:
<span class="docutils literal"><span class="pre">:math:`\psi(r)</span> = <span class="pre">\exp(-2r)`</span></span> will produce <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi>ψ</mi>
  <mo stretchy="false">(</mo>
  <mi>r</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mi>exp</mi>
  <mo stretchy="false">(</mo>
  <mo>-</mo>
  <mn>2</mn>
  <mi>r</mi>
  <mo stretchy="false">)</mo>
</mrow>
</math>.
Inside the backtics you can write anything you would write between dollar
signs in a LaTeX document.  <a class="brackets" href="#math-syntax" id="footnote-reference-2" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a></p>
<aside class="admonition tip">
<p class="admonition-title">Tip</p>
<p>If you put <span class="docutils literal">.. <span class="pre">default-role::</span> math</span> at the top of your
document, you can write <span class="docutils literal">`x^2`</span> instead of the longer
version: <span class="docutils literal"><span class="pre">:math:`x^2`</span></span>.  You can also introduce an
abbreviation like this <span class="docutils literal">.. role:: m(math)</span>.  That will allow
you to write <span class="docutils literal"><span class="pre">:m:`x^2`</span></span> or <span class="docutils literal"><span class="pre">`x^2`:m:</span></span>.</p>
</aside>
<p>The <strong>math directive</strong> is used for displayed equations. It corresponds to
an <span class="docutils literal">equation*</span> or <span class="docutils literal">align*</span> environment in a LaTeX document. If you
write:</p>
<pre class="literal-block">.. math:: \psi(r) = e^{-2r}</pre>
<p>you will get:</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <mi>ψ</mi>
  <mo stretchy="false">(</mo>
  <mi>r</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <msup>
    <mi>e</mi>
    <mrow>
      <mo>-</mo>
      <mn>2</mn>
      <mi>r</mi>
    </mrow>
  </msup>
</mrow>
</math>
</div>
<p>A more complex example is the definition of the <a class="reference internal" href="#fourier-transform">Fourier transform</a>:</p>
<pre class="literal-block">.. math::
   :name: Fourier transform

   (\mathcal{F}f)(y)
    = \frac{1}{\sqrt{2\pi}^{\ n}}
      \int_{\mathbb{R}^n} f(x)\,
      e^{-\mathrm{i} y \cdot x} \,\mathrm{d} x.</pre>
<p>which is rendered as:</p>
<div id="fourier-transform">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <mo stretchy="false">(</mo>
  <mi mathvariant="script">F</mi>
  <mi>f</mi>
  <mo stretchy="false">)</mo>
  <mo stretchy="false">(</mo>
  <mi>y</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mfrac>
    <mn>1</mn>
    <msup>
      <msqrt>
        <mn>2</mn>
        <mi>π</mi>
      </msqrt>
      <mrow>
        <mspace width="0.333em"/>
        <mi>n</mi>
      </mrow>
    </msup>
  </mfrac>
  <msub>
    <mo stretchy="false">∫</mo>
    <msup>
      <mi mathvariant="double-struck">R</mi>
      <mi>n</mi>
    </msup>
  </msub>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo rspace="0.167em" stretchy="false">)</mo>
  <msup>
    <mi>e</mi>
    <mrow>
      <mo>-</mo>
      <mi mathvariant="normal">i</mi>
      <mi>y</mi>
      <mo>⋅</mo>
      <mi>x</mi>
    </mrow>
  </msup>
  <mspace width="0.167em"/>
  <mi mathvariant="normal">d</mi>
  <mi>x</mi>
  <mo>.</mo>
</mrow>
</math>
</div>
<p>The <span class="docutils literal">:name:</span> option puts a label on the equation that can be
linked to by <a class="reference external" href="../ref/rst/restructuredtext.html#hyperlink-references">hyperlink references</a>.</p>
<p>Displayed equations can use <span class="docutils literal">\\</span> and <span class="docutils literal">&amp;</span> for line shifts and alignments:</p>
<pre class="literal-block">.. math::

 a &amp;= (x + y)^2         &amp;  b &amp;= (x - y)^2 \\
   &amp;= x^2 + 2xy + y^2   &amp;    &amp;= x^2 - 2xy + y^2</pre>
<p>LaTeX output will wrap it in an <span class="docutils literal">align*</span> environment.
The result is:</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mstyle scriptlevel="0">
  <mtable displaystyle="true" columnalign="right left right left" columnspacing="0.2em 1em 0.2em">
    <mtr>
      <mtd>
        <mi>a</mi>
      </mtd>
      <mtd>
        <mo>=</mo>
        <mo stretchy="false">(</mo>
        <mi>x</mi>
        <mo>+</mo>
        <mi>y</mi>
        <msup>
          <mo stretchy="false">)</mo>
          <mn>2</mn>
        </msup>
      </mtd>
      <mtd>
        <mi>b</mi>
      </mtd>
      <mtd>
        <mo>=</mo>
        <mo stretchy="false">(</mo>
        <mi>x</mi>
        <mo>-</mo>
        <mi>y</mi>
        <msup>
          <mo stretchy="false">)</mo>
          <mn>2</mn>
        </msup>
      </mtd>
    </mtr>
    <mtr>
      <mtd/>
      <mtd>
        <mo>=</mo>
        <msup>
          <mi>x</mi>
          <mn>2</mn>
        </msup>
        <mo>+</mo>
        <mn>2</mn>
        <mi>x</mi>
        <mi>y</mi>
        <mo>+</mo>
        <msup>
          <mi>y</mi>
          <mn>2</mn>
        </msup>
      </mtd>
      <mtd/>
      <mtd>
        <mo>=</mo>
        <msup>
          <mi>x</mi>
          <mn>2</mn>
        </msup>
        <mo>-</mo>
        <mn>2</mn>
        <mi>x</mi>
        <mi>y</mi>
        <mo>+</mo>
        <msup>
          <mi>y</mi>
          <mn>2</mn>
        </msup>
      </mtd>
    </mtr>
  </mtable>
</mstyle>
</math>
</div>
<p>The <span class="docutils literal">aligned</span> environment can be used as a component in a containing
expression. E.g.,</p>
<pre class="literal-block">.. math::
  \left.
    \begin{aligned}
      B' &amp; = -\partial\times E,         \\
      E' &amp; = \partial\times B - 4\pi j,
    \end{aligned}
  \right\}
  \qquad \text{Maxwell’s equations}</pre>
<p>results in</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <mrow>
    <mrow>
      <mstyle displaystyle="true">
        <mstyle scriptlevel="0">
          <mtable columnalign="right left" columnspacing="0.2em">
            <mtr>
              <mtd>
                <msup>
                  <mi>B</mi>
                  <mo>′</mo>
                </msup>
              </mtd>
              <mtd>
                <mo>=</mo>
                <mo>-</mo>
                <mi mathvariant="normal">∂</mi>
                <mo>×</mo>
                <mi>E</mi>
              </mtd>
            </mtr>
            <mtr>
              <mtd>
                <msup>
                  <mi>E</mi>
                  <mo>′</mo>
                </msup>
              </mtd>
              <mtd>
                <mo>=</mo>
                <mi mathvariant="normal">∂</mi>
                <mo>×</mo>
                <mi>B</mi>
                <mo>-</mo>
                <mn>4</mn>
                <mi>π</mi>
                <mi>j</mi>
              </mtd>
            </mtr>
          </mtable>
        </mstyle>
        <mstyle displaystyle="false">
          <mspace width="0.278em"/>
        </mstyle>
      </mstyle>
    </mrow>
    <mo stretchy="true">}</mo>
  </mrow>
  <mspace width="2.167em"/>
  <mtext>Maxwell’s equations.</mtext>
</mrow>
</math>
</div>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="math-syntax" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<span class="backrefs">(<a role="doc-backlink" href="#footnote-reference-1">1</a>,<a role="doc-backlink" href="#footnote-reference-2">2</a>)</span>
<p>The supported LaTeX commands include AMS extensions
(see, e.g., the <a class="reference external" href="https://mirrors.ctan.org/info/short-math-guide/short-math-guide.pdf">Short Math Guide</a>). Some of the shown symbols
require the &quot;amssymb&quot; <a class="reference external" href="../../user/latex.html#latex-document-classes-and-packages">LaTeX package</a> (or another package providing
the AMS symbol macros) when exported with the &quot;latex&quot; writer.</p>
<p>The support is limited to a subset of <em>LaTeX math</em> by the conversion
required for many output formats.  For HTML, the <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a>
configuration setting (or the corresponding <span class="docutils literal"><span class="pre">--math-output</span></span> command
line option) selects between alternative output formats with different
subsets of supported elements. If a writer does not support math
typesetting, the content is inserted verbatim.</p>
</aside>
</aside>
</section>
<section id="mathematical-symbols">
<h2><a class="toc-backref" href="#toc-entry-2" role="doc-backlink"><span class="sectnum">2 </span>Mathematical symbols</a></h2>
<p>The following tables are adapted from the first edition of
&quot;The LaTeX Companion&quot; (Goossens, Mittelbach, Samarin) and the
AMS <a class="reference external" href="https://mirrors.ctan.org/info/short-math-guide/short-math-guide.pdf">Short Math Guide</a>.</p>
<section id="accents-and-embellishments">
<h3><a class="toc-backref" href="#toc-entry-3" role="doc-backlink"><span class="sectnum">2.1 </span>Accents and embellishments</a></h3>
<p>The &quot;narrow&quot; accents are intended for a single-letter base.</p>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mi>x</mi>
  <mo accent="true">´</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\acute{x}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mi>t</mi>
  <mo accent="true">·</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\dot{t}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mi>x</mi>
  <mo accent="true">`</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\grave{x}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mi>x</mi>
  <mo stretchy="true" accent="true">⃗</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\vec{x}</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mi>v</mi>
  <mo accent="true">¯</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\bar{v}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mi>t</mi>
  <mo accent="true">··</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\ddot{t}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mi>x</mi>
  <mo accent="true">̂</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\hat{x}</span></p></td>
<td></td>
<td></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mi>x</mi>
  <mo stretchy="false" accent="true">˘</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\breve{x}</span></p></td>
<td><p><span class="math problematic m">\dddot{t}</span></p></td>
<td><p><span class="docutils literal">\dddot{t}</span></p></td>
<td><p><span class="math problematic m">\mathring{x}</span></p></td>
<td><p><span class="docutils literal">\mathring{x}</span></p></td>
<td></td>
<td></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mi>x</mi>
  <mo stretchy="false" accent="true">ˇ</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\check{x}</span></p></td>
<td><p><span class="math problematic m">\ddddot{t}</span></p></td>
<td><p><span class="docutils literal">\ddddot{t}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mi>n</mi>
  <mo stretchy="false" accent="true">˜</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\tilde{n}</span></p></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 150)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\dddot&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 150)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\mathring&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 151)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\ddddot&quot;</p>
</aside>
<p>When adding an accent to an i or j in math, dotless variants can be
obtained with <span class="docutils literal">\imath</span> and <span class="docutils literal">\jmath</span>: <math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mi>ı</mi>
  <mo accent="true">̂</mo>
</mover>
</math>, <math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mi>𝚥</mi>
  <mo stretchy="true" accent="true">⃗</mo>
</mover>
</math>.</p>
<p>For embellishments that span multiple symbols, use:</p>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mrow>
    <mi>g</mi>
    <mi>b</mi>
    <mi>i</mi>
  </mrow>
  <mo stretchy="true" accent="true">˜</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\widetilde{gbi}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mrow>
    <mi>g</mi>
    <mi>b</mi>
    <mi>i</mi>
  </mrow>
  <mo stretchy="true" accent="true">̂</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\widehat{gbi}</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mrow>
    <mi>g</mi>
    <mi>b</mi>
    <mi>i</mi>
  </mrow>
  <mo stretchy="true" accent="true">¯</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\overline{gbi}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<munder>
  <mrow>
    <mi>g</mi>
    <mi>b</mi>
    <mi>i</mi>
  </mrow>
  <mo stretchy="true" accent="true">¯</mo>
</munder>
</math></p></td>
<td><p><span class="docutils literal">\underline{gbi}</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mrow>
    <mi>g</mi>
    <mi>b</mi>
    <mi>i</mi>
  </mrow>
  <mo stretchy="true" accent="false">︷</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\overbrace{gbi}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<munder>
  <mrow>
    <mi>g</mi>
    <mi>b</mi>
    <mi>i</mi>
  </mrow>
  <mo stretchy="true" accent="false">︸</mo>
</munder>
</math></p></td>
<td><p><span class="docutils literal">\underbrace{gbi}</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mrow>
    <mi>g</mi>
    <mi>b</mi>
    <mi>i</mi>
  </mrow>
  <mo stretchy="true" accent="true">←</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\overleftarrow{gbi}</span></p></td>
<td><p><span class="math problematic m">\underleftarrow{gbi}</span></p></td>
<td><p><span class="docutils literal">\underleftarrow{gbi}</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mrow>
    <mi>g</mi>
    <mi>b</mi>
    <mi>i</mi>
  </mrow>
  <mo stretchy="true" accent="true">→</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\overrightarrow{gbi}</span></p></td>
<td><p><span class="math problematic m">\underrightarrow{gbi}</span></p></td>
<td><p><span class="docutils literal">\underrightarrow{gbi}</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mrow>
    <mi>g</mi>
    <mi>b</mi>
    <mi>i</mi>
  </mrow>
  <mo stretchy="true" accent="true">↔</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\overleftrightarrow{gbi}</span></p></td>
<td><p><span class="math problematic m">\underleftrightarrow{gbi}</span></p></td>
<td><p><span class="docutils literal">\underleftrightarrow{gbi}</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 165)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\underleftarrow&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 166)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\underrightarrow&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 167)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\underleftrightarrow&quot;</p>
</aside>
</section>
<section id="binary-operators">
<h3><a class="toc-backref" href="#toc-entry-4" role="doc-backlink"><span class="sectnum">2.2 </span>Binary operators</a></h3>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>*</mo>
</math></p></td>
<td><p><span class="docutils literal">*</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊛</mo>
</math></p></td>
<td><p><span class="docutils literal">\circledast</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊖</mo>
</math></p></td>
<td><p><span class="docutils literal">\ominus</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>+</mo>
</math></p></td>
<td><p><span class="docutils literal">+</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊚</mo>
</math></p></td>
<td><p><span class="docutils literal">\circledcirc</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊕</mo>
</math></p></td>
<td><p><span class="docutils literal">\oplus</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>-</mo>
</math></p></td>
<td><p><span class="docutils literal">-</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊝</mo>
</math></p></td>
<td><p><span class="docutils literal">\circleddash</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊘</mo>
</math></p></td>
<td><p><span class="docutils literal">\oslash</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>:</mo>
</math></p></td>
<td><p><span class="docutils literal">:</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∪</mo>
</math></p></td>
<td><p><span class="docutils literal">\cup</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊗</mo>
</math></p></td>
<td><p><span class="docutils literal">\otimes</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋒</mo>
</math></p></td>
<td><p><span class="docutils literal">\Cap</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋎</mo>
</math></p></td>
<td><p><span class="docutils literal">\curlyvee</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>±</mo>
</math></p></td>
<td><p><span class="docutils literal">\pm</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋓</mo>
</math></p></td>
<td><p><span class="docutils literal">\Cup</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋏</mo>
</math></p></td>
<td><p><span class="docutils literal">\curlywedge</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋌</mo>
</math></p></td>
<td><p><span class="docutils literal">\rightthreetimes</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⨿</mo>
</math></p></td>
<td><p><span class="docutils literal">\amalg</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>†</mo>
</math></p></td>
<td><p><span class="docutils literal">\dagger</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋊</mo>
</math></p></td>
<td><p><span class="docutils literal">\rtimes</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>*</mo>
</math></p></td>
<td><p><span class="docutils literal">\ast</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>‡</mo>
</math></p></td>
<td><p><span class="docutils literal">\ddagger</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">∖</mo>
</math></p></td>
<td><p><span class="docutils literal">\setminus</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>◯</mo>
</math></p></td>
<td><p><span class="docutils literal">\bigcirc</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋄</mo>
</math></p></td>
<td><p><span class="docutils literal">\diamond</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">∖</mo>
</math></p></td>
<td><p><span class="docutils literal">\smallsetminus</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>▽</mo>
</math></p></td>
<td><p><span class="docutils literal">\bigtriangledown</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>÷</mo>
</math></p></td>
<td><p><span class="docutils literal">\div</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊓</mo>
</math></p></td>
<td><p><span class="docutils literal">\sqcap</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>△</mo>
</math></p></td>
<td><p><span class="docutils literal">\bigtriangleup</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋇</mo>
</math></p></td>
<td><p><span class="docutils literal">\divideontimes</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊔</mo>
</math></p></td>
<td><p><span class="docutils literal">\sqcup</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊡</mo>
</math></p></td>
<td><p><span class="docutils literal">\boxdot</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∔</mo>
</math></p></td>
<td><p><span class="docutils literal">\dotplus</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋆</mo>
</math></p></td>
<td><p><span class="docutils literal">\star</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊟</mo>
</math></p></td>
<td><p><span class="docutils literal">\boxminus</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⌆</mo>
</math></p></td>
<td><p><span class="docutils literal">\doublebarwedge</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>×</mo>
</math></p></td>
<td><p><span class="docutils literal">\times</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊞</mo>
</math></p></td>
<td><p><span class="docutils literal">\boxplus</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋗</mo>
</math></p></td>
<td><p><span class="docutils literal">\gtrdot</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>◃</mo>
</math></p></td>
<td><p><span class="docutils literal">\triangleleft</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊠</mo>
</math></p></td>
<td><p><span class="docutils literal">\boxtimes</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊺</mo>
</math></p></td>
<td><p><span class="docutils literal">\intercal</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>▹</mo>
</math></p></td>
<td><p><span class="docutils literal">\triangleright</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>•</mo>
</math></p></td>
<td><p><span class="docutils literal">\bullet</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋋</mo>
</math></p></td>
<td><p><span class="docutils literal">\leftthreetimes</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊎</mo>
</math></p></td>
<td><p><span class="docutils literal">\uplus</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∩</mo>
</math></p></td>
<td><p><span class="docutils literal">\cap</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋖</mo>
</math></p></td>
<td><p><span class="docutils literal">\lessdot</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∨</mo>
</math></p></td>
<td><p><span class="docutils literal">\vee</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋅</mo>
</math></p></td>
<td><p><span class="docutils literal">\cdot</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋉</mo>
</math></p></td>
<td><p><span class="docutils literal">\ltimes</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊻</mo>
</math></p></td>
<td><p><span class="docutils literal">\veebar</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋅</mo>
</math></p></td>
<td><p><span class="docutils literal">\centerdot</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∓</mo>
</math></p></td>
<td><p><span class="docutils literal">\mp</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∧</mo>
</math></p></td>
<td><p><span class="docutils literal">\wedge</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∘</mo>
</math></p></td>
<td><p><span class="docutils literal">\circ</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊙</mo>
</math></p></td>
<td><p><span class="docutils literal">\odot</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≀</mo>
</math></p></td>
<td><p><span class="docutils literal">\wr</span></p></td>
</tr>
</tbody>
</table>
</section>
<section id="extensible-delimiters">
<h3><a class="toc-backref" href="#toc-entry-5" role="doc-backlink"><span class="sectnum">2.3 </span>Extensible delimiters</a></h3>
<p>Unless you indicate otherwise, delimiters in math formulas remain at the
standard size regardless of the height of the enclosed material. To get
adaptable sizes, use <span class="docutils literal">\left</span> and <span class="docutils literal">\right</span> prefixes, for example
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi>g</mi>
  <mo stretchy="false">(</mo>
  <mi>A</mi>
  <mo>,</mo>
  <mi>B</mi>
  <mo>,</mo>
  <mi>Y</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mi>f</mi>
  <mspace width="0.167em"/>
  <mrow>
    <mo stretchy="true">(</mo>
    <mrow>
      <mi>A</mi>
      <mo>,</mo>
      <mi>B</mi>
      <mo>,</mo>
      <mi>X</mi>
      <mo>=</mo>
      <msup>
        <mi>h</mi>
        <mrow>
          <mo stretchy="false">[</mo>
          <mi>X</mi>
          <mo stretchy="false">]</mo>
        </mrow>
      </msup>
      <mo stretchy="false">(</mo>
      <mi>Y</mi>
      <mo stretchy="false">)</mo>
    </mrow>
    <mo stretchy="true">)</mo>
  </mrow>
</mrow>
</math> or</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <msub>
    <mi>a</mi>
    <mi>n</mi>
  </msub>
  <mo>=</mo>
  <msup>
    <mrow>
      <mo stretchy="true">(</mo>
      <mrow>
        <mfrac>
          <mn>1</mn>
          <mn>2</mn>
        </mfrac>
      </mrow>
      <mo stretchy="true">)</mo>
    </mrow>
    <mi>n</mi>
  </msup>
</mrow>
</math>
</div>
<p>Use <span class="docutils literal">.</span> for &quot;empty&quot; delimiters:</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <mi>A</mi>
  <mo>=</mo>
  <msubsup>
    <mrow>
      <mrow>
        <mfrac>
          <mn>1</mn>
          <mrow>
            <mn>1</mn>
            <mo>-</mo>
            <mi>n</mi>
          </mrow>
        </mfrac>
        <mspace width="0.167em"/>
      </mrow>
      <mo stretchy="true">|</mo>
    </mrow>
    <mrow>
      <mi>n</mi>
      <mo>=</mo>
      <mn>0</mn>
    </mrow>
    <mi mathvariant="normal">∞</mi>
  </msubsup>
</mrow>
</math>
</div>
<p>See also the commands for fixed <a class="reference internal" href="#delimiter-sizes">delimiter sizes</a> below.</p>
<p>The following symbols extend when used with <span class="docutils literal">\left</span> and <span class="docutils literal">\right</span>:</p>
<section id="pairing-delimiters">
<h4><a class="toc-backref" href="#toc-entry-6" role="doc-backlink"><span class="sectnum">2.3.1 </span>Pairing delimiters</a></h4>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="false">(</mo>
  <mo stretchy="false">)</mo>
</mrow>
</math></p></td>
<td><p><span class="docutils literal">( )</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="false">〈</mo>
  <mo stretchy="false">〉</mo>
</mrow>
</math></p></td>
<td><p><span class="docutils literal">\langle \rangle</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="false">[</mo>
  <mo stretchy="false">]</mo>
</mrow>
</math></p></td>
<td><p><span class="docutils literal">[ ]</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="false">⌈</mo>
  <mo stretchy="false">⌉</mo>
</mrow>
</math></p></td>
<td><p><span class="docutils literal">\lceil \rceil</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="false">{</mo>
  <mo stretchy="false">}</mo>
</mrow>
</math></p></td>
<td><p><span class="docutils literal">\{ \}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="false">⌊</mo>
  <mo stretchy="false">⌋</mo>
</mrow>
</math></p></td>
<td><p><span class="docutils literal">\lfloor \rfloor</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="false">|</mo>
  <mo stretchy="false">|</mo>
</mrow>
</math></p></td>
<td><p><span class="docutils literal">\lvert \rvert</span></p></td>
<td><p><span class="math problematic m">\lgroup \rgroup</span></p></td>
<td><p><span class="docutils literal">\lgroup \rgroup</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo>∥</mo>
  <mo>∥</mo>
</mrow>
</math></p></td>
<td><p><span class="docutils literal">\lVert \rVert</span></p></td>
<td><p><span class="math problematic m">\lmoustache \rmoustache</span></p></td>
<td><p><span class="docutils literal">\lmoustache \rmoustache</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 224)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\lgroup&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 225)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\lmoustache&quot;</p>
</aside>
</section>
<section id="nonpairing-delimiters">
<h4><a class="toc-backref" href="#toc-entry-7" role="doc-backlink"><span class="sectnum">2.3.2 </span>Nonpairing delimiters</a></h4>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">|</mo>
</math></p></td>
<td><p><span class="docutils literal">|</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">|</mo>
</math></p></td>
<td><p><span class="docutils literal">\vert</span></p></td>
<td><p><span class="math problematic m">\arrowvert</span></p></td>
<td><p><span class="docutils literal">\arrowvert</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∥</mo>
</math></p></td>
<td><p><span class="docutils literal">\|</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∥</mo>
</math></p></td>
<td><p><span class="docutils literal">\Vert</span></p></td>
<td><p><span class="math problematic m">\Arrowvert</span></p></td>
<td><p><span class="docutils literal">\Arrowvert</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">/</mo>
</math></p></td>
<td><p><span class="docutils literal">/</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">∖</mo>
</math></p></td>
<td><p><span class="docutils literal">\backslash</span></p></td>
<td><p><span class="math problematic m">\bracevert</span></p></td>
<td><p><span class="docutils literal">\bracevert</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 234)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\arrowvert&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 235)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\Arrowvert&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 236)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\bracevert&quot;</p>
</aside>
<p>The use of <span class="docutils literal">|</span> and <span class="docutils literal">\|</span> for pairs of vertical bars may produce
incorrect spacing, e.g., <span class="docutils literal"><span class="pre">|k|=|-k|</span></span> produces <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="false">|</mo>
  <mi>k</mi>
  <mo stretchy="false">|</mo>
  <mo>=</mo>
  <mo stretchy="false">|</mo>
  <mo>-</mo>
  <mi>k</mi>
  <mo stretchy="false">|</mo>
</mrow>
</math> and
<span class="docutils literal">|\sin(x)|</span> produces <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="false">|</mo>
  <mi>sin</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo stretchy="false">|</mo>
</mrow>
</math>. The pairing delimiters, e.g.
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="false">|</mo>
  <mo>-</mo>
  <mi>k</mi>
  <mo stretchy="false">|</mo>
</mrow>
</math> and <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="false">|</mo>
  <mi>sin</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo stretchy="false">|</mo>
</mrow>
</math>, prevent this problem.</p>
</section>
</section>
<section id="extensible-vertical-arrows">
<h3><a class="toc-backref" href="#toc-entry-8" role="doc-backlink"><span class="sectnum">2.4 </span>Extensible vertical arrows</a></h3>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↑</mo>
</math>     <span class="docutils literal">\uparrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇑</mo>
</math>     <span class="docutils literal">\Uparrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↓</mo>
</math>   <span class="docutils literal">\downarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇓</mo>
</math>   <span class="docutils literal">\Downarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↕</mo>
</math> <span class="docutils literal">\updownarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇕</mo>
</math> <span class="docutils literal">\Updownarrow</span></p></td>
</tr>
</tbody>
</table>
</section>
<section id="functions-named-operators">
<h3><a class="toc-backref" href="#toc-entry-9" role="doc-backlink"><span class="sectnum">2.5 </span>Functions (named operators)</a></h3>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>arccos</mi>
</math></p></td>
<td><p><span class="docutils literal">\arccos</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>gcd</mo>
</math></p></td>
<td><p><span class="docutils literal">\gcd</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>Pr</mo>
</math></p></td>
<td><p><span class="docutils literal">\Pr</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>arcsin</mi>
</math></p></td>
<td><p><span class="docutils literal">\arcsin</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>hom</mi>
</math></p></td>
<td><p><span class="docutils literal">\hom</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>proj lim</mo>
</math></p></td>
<td><p><span class="docutils literal">\projlim</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>arctan</mi>
</math></p></td>
<td><p><span class="docutils literal">\arctan</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>inf</mo>
</math></p></td>
<td><p><span class="docutils literal">\inf</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>sec</mi>
</math></p></td>
<td><p><span class="docutils literal">\sec</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>arg</mi>
</math></p></td>
<td><p><span class="docutils literal">\arg</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>inj lim</mo>
</math></p></td>
<td><p><span class="docutils literal">\injlim</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>sin</mi>
</math></p></td>
<td><p><span class="docutils literal">\sin</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>cos</mi>
</math></p></td>
<td><p><span class="docutils literal">\cos</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ker</mi>
</math></p></td>
<td><p><span class="docutils literal">\ker</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>sinh</mi>
</math></p></td>
<td><p><span class="docutils literal">\sinh</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>cosh</mi>
</math></p></td>
<td><p><span class="docutils literal">\cosh</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>lg</mi>
</math></p></td>
<td><p><span class="docutils literal">\lg</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>sup</mo>
</math></p></td>
<td><p><span class="docutils literal">\sup</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>cot</mi>
</math></p></td>
<td><p><span class="docutils literal">\cot</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>lim</mo>
</math></p></td>
<td><p><span class="docutils literal">\lim</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>tan</mi>
</math></p></td>
<td><p><span class="docutils literal">\tan</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>coth</mi>
</math></p></td>
<td><p><span class="docutils literal">\coth</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>lim inf</mo>
</math></p></td>
<td><p><span class="docutils literal">\liminf</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>tanh</mi>
</math></p></td>
<td><p><span class="docutils literal">\tanh</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>csc</mi>
</math></p></td>
<td><p><span class="docutils literal">\csc</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>lim sup</mo>
</math></p></td>
<td><p><span class="docutils literal">\limsup</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mo movablelimits="false">lim</mo>
  <mo stretchy="true" accent="true">¯</mo>
</mover>
</math></p></td>
<td><p><span class="docutils literal">\varlimsup</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>deg</mi>
</math></p></td>
<td><p><span class="docutils literal">\deg</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ln</mi>
</math></p></td>
<td><p><span class="docutils literal">\ln</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<munder>
  <mo movablelimits="false">lim</mo>
  <mo stretchy="true" accent="true">¯</mo>
</munder>
</math></p></td>
<td><p><span class="docutils literal">\varliminf</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>det</mo>
</math></p></td>
<td><p><span class="docutils literal">\det</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>log</mi>
</math></p></td>
<td><p><span class="docutils literal">\log</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<munder>
  <mo movablelimits="false">lim</mo>
  <mo accent="true">←</mo>
</munder>
</math></p></td>
<td><p><span class="docutils literal">\varprojlim</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>dim</mi>
</math></p></td>
<td><p><span class="docutils literal">\dim</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>max</mo>
</math></p></td>
<td><p><span class="docutils literal">\max</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<munder>
  <mo movablelimits="false">lim</mo>
  <mo accent="true">→</mo>
</munder>
</math></p></td>
<td><p><span class="docutils literal">\varinjlim</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>exp</mi>
</math></p></td>
<td><p><span class="docutils literal">\exp</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>min</mo>
</math></p></td>
<td><p><span class="docutils literal">\min</span></p></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<p>Named operators outside the above list can be typeset with
<span class="docutils literal">\operatorname{name}</span>, e.g.</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <mi>sgn</mi>
  <mo stretchy="false">(</mo>
  <mo>-</mo>
  <mn>3</mn>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mo>-</mo>
  <mn>1</mn>
  <mo>.</mo>
</mrow>
</math>
</div>
<!-- TODO: \operatorname* for function name with limits. -->
<p>The <span class="docutils literal">\DeclareMathOperator</span> command can only be used in the
<a class="reference external" href="latex.html#latex-preamble">LaTeX preamble</a>.</p>
</section>
<section id="greek-letters">
<h3><a class="toc-backref" href="#toc-entry-10" role="doc-backlink"><span class="sectnum">2.6 </span>Greek letters</a></h3>
<p>Greek letters that have Latin look-alikes are rarely used in math
formulas and not supported by LaTeX.</p>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">Γ</mi>
</math></p></td>
<td><p><span class="docutils literal">\Gamma</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>α</mi>
</math></p></td>
<td><p><span class="docutils literal">\alpha</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>μ</mi>
</math></p></td>
<td><p><span class="docutils literal">\mu</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ω</mi>
</math></p></td>
<td><p><span class="docutils literal">\omega</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">Δ</mi>
</math></p></td>
<td><p><span class="docutils literal">\Delta</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>β</mi>
</math></p></td>
<td><p><span class="docutils literal">\beta</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ν</mi>
</math></p></td>
<td><p><span class="docutils literal">\nu</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ϝ</mi>
</math></p></td>
<td><p><span class="docutils literal">\digamma</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">Λ</mi>
</math></p></td>
<td><p><span class="docutils literal">\Lambda</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>γ</mi>
</math></p></td>
<td><p><span class="docutils literal">\gamma</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ξ</mi>
</math></p></td>
<td><p><span class="docutils literal">\xi</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ε</mi>
</math></p></td>
<td><p><span class="docutils literal">\varepsilon</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">Φ</mi>
</math></p></td>
<td><p><span class="docutils literal">\Phi</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>δ</mi>
</math></p></td>
<td><p><span class="docutils literal">\delta</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>π</mi>
</math></p></td>
<td><p><span class="docutils literal">\pi</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ϰ</mi>
</math></p></td>
<td><p><span class="docutils literal">\varkappa</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">Π</mi>
</math></p></td>
<td><p><span class="docutils literal">\Pi</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ϵ</mi>
</math></p></td>
<td><p><span class="docutils literal">\epsilon</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ρ</mi>
</math></p></td>
<td><p><span class="docutils literal">\rho</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>φ</mi>
</math></p></td>
<td><p><span class="docutils literal">\varphi</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">Ψ</mi>
</math></p></td>
<td><p><span class="docutils literal">\Psi</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ζ</mi>
</math></p></td>
<td><p><span class="docutils literal">\zeta</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>σ</mi>
</math></p></td>
<td><p><span class="docutils literal">\sigma</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ϖ</mi>
</math></p></td>
<td><p><span class="docutils literal">\varpi</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">Σ</mi>
</math></p></td>
<td><p><span class="docutils literal">\Sigma</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>η</mi>
</math></p></td>
<td><p><span class="docutils literal">\eta</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>τ</mi>
</math></p></td>
<td><p><span class="docutils literal">\tau</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ϱ</mi>
</math></p></td>
<td><p><span class="docutils literal">\varrho</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">Θ</mi>
</math></p></td>
<td><p><span class="docutils literal">\Theta</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>θ</mi>
</math></p></td>
<td><p><span class="docutils literal">\theta</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>υ</mi>
</math></p></td>
<td><p><span class="docutils literal">\upsilon</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ς</mi>
</math></p></td>
<td><p><span class="docutils literal">\varsigma</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">Υ</mi>
</math></p></td>
<td><p><span class="docutils literal">\Upsilon</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ι</mi>
</math></p></td>
<td><p><span class="docutils literal">\iota</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ϕ</mi>
</math></p></td>
<td><p><span class="docutils literal">\phi</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ϑ</mi>
</math></p></td>
<td><p><span class="docutils literal">\vartheta</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">Ξ</mi>
</math></p></td>
<td><p><span class="docutils literal">\Xi</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>κ</mi>
</math></p></td>
<td><p><span class="docutils literal">\kappa</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>χ</mi>
</math></p></td>
<td><p><span class="docutils literal">\chi</span></p></td>
<td></td>
<td></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">Ω</mi>
</math></p></td>
<td><p><span class="docutils literal">\Omega</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>λ</mi>
</math></p></td>
<td><p><span class="docutils literal">\lambda</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ψ</mi>
</math></p></td>
<td><p><span class="docutils literal">\psi</span></p></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<p>In LaTeX, the default font for capital Greek letters is upright/roman.
<em>Italic</em> capital Greek letters can be obtained by loading a <a class="reference external" href="https://mirrors.ctan.org/macros/latex/contrib/isomath/isomath.html#table-2">package
providing the &quot;ISO&quot; math style</a>. They are used by default in MathML.</p>
<p>Individual Greek italic capitals can also be achieved preceding the
letter name with <span class="docutils literal">var</span> like <span class="docutils literal">\varPhi</span>:
<span class="math problematic m">\varGamma\ \varDelta\ \varLambda\ \varPhi\ \varPi\ \varPsi\ \varSigma\
\varTheta\ \varUpsilon\ \varXi\ \varOmega</span></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 315)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\varGamma&quot;</p>
</aside>
</section>
<section id="letterlike-symbols">
<h3><a class="toc-backref" href="#toc-entry-11" role="doc-backlink"><span class="sectnum">2.7 </span>Letterlike symbols</a></h3>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∀</mo>
</math></p></td>
<td><p><span class="docutils literal">\forall</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">ℵ</mi>
</math></p></td>
<td><p><span class="docutils literal">\aleph</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">ħ</mi>
</math></p></td>
<td><p><span class="docutils literal">\hbar</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ℓ</mi>
</math></p></td>
<td><p><span class="docutils literal">\ell</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∁</mo>
</math></p></td>
<td><p><span class="docutils literal">\complement</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">ℶ</mi>
</math></p></td>
<td><p><span class="docutils literal">\beth</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">ℏ</mi>
</math></p></td>
<td><p><span class="docutils literal">\hslash</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>℘</mi>
</math></p></td>
<td><p><span class="docutils literal">\wp</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∃</mo>
</math></p></td>
<td><p><span class="docutils literal">\exists</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">ℷ</mi>
</math></p></td>
<td><p><span class="docutils literal">\gimel</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">ℑ</mi>
</math></p></td>
<td><p><span class="docutils literal">\Im</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">ℜ</mi>
</math></p></td>
<td><p><span class="docutils literal">\Re</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">Ⅎ</mi>
</math></p></td>
<td><p><span class="docutils literal">\Finv</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">ℸ</mi>
</math></p></td>
<td><p><span class="docutils literal">\daleth</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>ı</mi>
</math></p></td>
<td><p><span class="docutils literal">\imath</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">®</mi>
</math></p></td>
<td><p><span class="docutils literal">\circledR</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">⅁</mi>
</math></p></td>
<td><p><span class="docutils literal">\Game</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">∂</mi>
</math></p></td>
<td><p><span class="docutils literal">\partial</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi>𝚥</mi>
</math></p></td>
<td><p><span class="docutils literal">\jmath</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">Ⓢ</mi>
</math></p></td>
<td><p><span class="docutils literal">\circledS</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">℧</mi>
</math></p></td>
<td><p><span class="docutils literal">\mho</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">ð</mi>
</math></p></td>
<td><p><span class="docutils literal">\eth</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">𝕜</mi>
</math></p></td>
<td><p><span class="docutils literal">\Bbbk</span></p></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
</section>
<section id="math-alphabets">
<span id="math-alphabet"></span><h3><a class="toc-backref" href="#toc-entry-12" role="doc-backlink"><span class="sectnum">2.8 </span>Math alphabets</a></h3>
<p>The TeX <em>math alphabet</em> macros are intended for mathematical variables
where style variations are important semantically.
They style letters and numbers with a combination of font attributes
(shape, weight, family) --- non-alphanumerical symbols, function names,
and mathematical text are left unchanged.</p>
<p>MathML uses the <em>mathvariant</em> <a class="reference external" href="https://www.w3.org/TR/mathml4/#presm_commatt">style attribute</a> or pre-styled characters
from the <a class="reference external" href="https://en.wikipedia.org/wiki/Mathematical_Alphanumeric_Symbols">Mathematical Alphanumeric Symbols</a> Unicode block.</p>
<table>
<thead>
<tr><th class="head"><p>command</p></th>
<th class="head"><p>example</p></th>
<th class="head"><p>result</p></th>
</tr>
</thead>
<tbody>
<tr><td><p><span class="docutils literal">\mathrm</span></p></td>
<td><p><span class="docutils literal">s_\mathrm{out}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
  <mi>s</mi>
  <mi>out</mi>
</msub>
</math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathbf</span></p></td>
<td><p><span class="docutils literal"><span class="pre">\mathbf{r}^2=x^2+y^2</span></span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <msup>
    <mi mathvariant="bold">r</mi>
    <mn>2</mn>
  </msup>
  <mo>=</mo>
  <msup>
    <mi>x</mi>
    <mn>2</mn>
  </msup>
  <mo>+</mo>
  <msup>
    <mi>y</mi>
    <mn>2</mn>
  </msup>
</mrow>
</math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathit</span></p></td>
<td><p><span class="docutils literal"><span class="pre">\mathit{\sin\Gamma}</span></span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi>sin</mi>
  <mspace width="0.167em"/>
  <mi>Γ</mi>
</mrow>
</math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathcal</span></p></td>
<td><p><span class="docutils literal">\mathcal{F}f(x)</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi mathvariant="script">F</mi>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</mrow>
</math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathbb</span></p></td>
<td><p><span class="docutils literal">\mathbb{R \subset C}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi mathvariant="double-struck">R</mi>
  <mo>⊂</mo>
  <mi mathvariant="double-struck">C</mi>
</mrow>
</math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathfrak</span></p></td>
<td><p><span class="docutils literal">\mathfrak{a+b}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi mathvariant="fraktur">a</mi>
  <mo>+</mo>
  <mi mathvariant="fraktur">b</mi>
</mrow>
</math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathsf</span></p></td>
<td><p><span class="docutils literal">\mathsf x</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="sans-serif">x</mi>
</math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mathtt</span></p></td>
<td><p><span class="docutils literal">\mathtt{0.12}</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mn mathvariant="monospace">0</mn>
  <mo>.</mo>
  <mn mathvariant="monospace">12</mn>
</mrow>
</math></p></td>
</tr>
</tbody>
</table>
<p>The set of characters in a given &quot;math alphabet&quot; varies.
LaTeX may produce garbage for unsupported characters.
Additional math alphabets are defined in LaTeX packages, e.g.,</p>
<ul class="simple">
<li><p><span class="docutils literal">\mathbfit</span> from <a class="reference external" href="https://www.ctan.org/pkg/isomath">isomath</a> allows vector symbols in line with the
International Standard <a class="citation-reference" href="#iso-80000-2" id="citation-reference-1" role="doc-biblioref">[ISO-80000-2]</a>.
E.g., <span class="docutils literal"><span class="pre">\mathbfit{r}^2=x^2+y^2</span></span> becomes <span class="math problematic m">\mathbfit{r}^2=x^2+y^2</span>.</p></li>
<li><p>Several packages, e.g. <a class="reference external" href="https://www.ctan.org/pkg/mathrsfs">mathrsfs</a>, define <span class="docutils literal">\mathscr</span> that selects a
differently shaped &quot;script&quot; alphabet.</p></li>
</ul>
<p>The listing below shows the characters supported by Unicode and
Docutils with <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a> MathML. <a class="brackets" href="#italic-digits" id="footnote-reference-3" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 371)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\mathbfit&quot;</p>
</aside>
<dl class="simple">
<dt>default:</dt>
<dd><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi>A</mi>
  <mi>B</mi>
  <mi>C</mi>
  <mi>D</mi>
  <mi>E</mi>
  <mi>F</mi>
  <mi>G</mi>
  <mi>H</mi>
  <mi>I</mi>
  <mi>J</mi>
  <mi>K</mi>
  <mi>L</mi>
  <mi>M</mi>
  <mi>N</mi>
  <mi>O</mi>
  <mi>P</mi>
  <mi>Q</mi>
  <mi>R</mi>
  <mi>S</mi>
  <mi>T</mi>
  <mi>U</mi>
  <mi>V</mi>
  <mi>W</mi>
  <mi>X</mi>
  <mi>Y</mi>
  <mi>Z</mi>
  <mspace width="0.333em"/>
  <mi>a</mi>
  <mi>b</mi>
  <mi>c</mi>
  <mi>d</mi>
  <mi>e</mi>
  <mi>f</mi>
  <mi>g</mi>
  <mi>h</mi>
  <mi>i</mi>
  <mi>j</mi>
  <mi>k</mi>
  <mi>l</mi>
  <mi>m</mi>
  <mi>n</mi>
  <mi>o</mi>
  <mi>p</mi>
  <mi>q</mi>
  <mi>r</mi>
  <mi>s</mi>
  <mi>t</mi>
  <mi>u</mi>
  <mi>v</mi>
  <mi>w</mi>
  <mi>x</mi>
  <mi>y</mi>
  <mi>z</mi>
  <mspace width="0.333em"/>
  <mi>ı</mi>
  <mi>𝚥</mi>
</mrow>
</math>
<span class="math problematic m">{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖϜϝ\ \partial∇}</span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mn>0123456789</mn>
</math></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 382)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Non-ASCII characters may only be used in text mode (try enclosing the problem characters in &quot;\text{...}&quot;)</p>
</aside>
</dd>
<dt>mathrm:</dt>
<dd><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi>ABCDEFGHIJKLMNOPQRSTUVWXYZ</mi>
  <mspace width="0.333em"/>
  <mi>abcdefghijklmnopqrstuvwxyz</mi>
  <mspace width="0.333em"/>
  <mi>ı</mi>
  <mi>𝚥</mi>
</mrow>
</math>
<span class="math problematic m">\mathrm{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖϜϝ\ \partial∇}</span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mn>0123456789</mn>
</math></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 386)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Non-ASCII characters may only be used in text mode (try enclosing the problem characters in &quot;\text{...}&quot;)</p>
</aside>
</dd>
<dt>mathbf:</dt>
<dd><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi mathvariant="bold">A</mi>
  <mi mathvariant="bold">B</mi>
  <mi mathvariant="bold">C</mi>
  <mi mathvariant="bold">D</mi>
  <mi mathvariant="bold">E</mi>
  <mi mathvariant="bold">F</mi>
  <mi mathvariant="bold">G</mi>
  <mi mathvariant="bold">H</mi>
  <mi mathvariant="bold">I</mi>
  <mi mathvariant="bold">J</mi>
  <mi mathvariant="bold">K</mi>
  <mi mathvariant="bold">L</mi>
  <mi mathvariant="bold">M</mi>
  <mi mathvariant="bold">N</mi>
  <mi mathvariant="bold">O</mi>
  <mi mathvariant="bold">P</mi>
  <mi mathvariant="bold">Q</mi>
  <mi mathvariant="bold">R</mi>
  <mi mathvariant="bold">S</mi>
  <mi mathvariant="bold">T</mi>
  <mi mathvariant="bold">U</mi>
  <mi mathvariant="bold">V</mi>
  <mi mathvariant="bold">W</mi>
  <mi mathvariant="bold">X</mi>
  <mi mathvariant="bold">Y</mi>
  <mi mathvariant="bold">Z</mi>
  <mspace width="0.333em"/>
  <mi mathvariant="bold">a</mi>
  <mi mathvariant="bold">b</mi>
  <mi mathvariant="bold">c</mi>
  <mi mathvariant="bold">d</mi>
  <mi mathvariant="bold">e</mi>
  <mi mathvariant="bold">f</mi>
  <mi mathvariant="bold">g</mi>
  <mi mathvariant="bold">h</mi>
  <mi mathvariant="bold">i</mi>
  <mi mathvariant="bold">j</mi>
  <mi mathvariant="bold">k</mi>
  <mi mathvariant="bold">l</mi>
  <mi mathvariant="bold">m</mi>
  <mi mathvariant="bold">n</mi>
  <mi mathvariant="bold">o</mi>
  <mi mathvariant="bold">p</mi>
  <mi mathvariant="bold">q</mi>
  <mi mathvariant="bold">r</mi>
  <mi mathvariant="bold">s</mi>
  <mi mathvariant="bold">t</mi>
  <mi mathvariant="bold">u</mi>
  <mi mathvariant="bold">v</mi>
  <mi mathvariant="bold">w</mi>
  <mi mathvariant="bold">x</mi>
  <mi mathvariant="bold">y</mi>
  <mi mathvariant="bold">z</mi>
</mrow>
</math>
<span class="math problematic m">\mathbf{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖϜϝ\ \partial∇}</span>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mn mathvariant="bold">0123456789</mn>
</math></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 390)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Non-ASCII characters may only be used in text mode (try enclosing the problem characters in &quot;\text{...}&quot;)</p>
</aside>
</dd>
<dt>mathit:</dt>
<dd><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi>A</mi>
  <mi>B</mi>
  <mi>C</mi>
  <mi>D</mi>
  <mi>E</mi>
  <mi>F</mi>
  <mi>G</mi>
  <mi>H</mi>
  <mi>I</mi>
  <mi>J</mi>
  <mi>K</mi>
  <mi>L</mi>
  <mi>M</mi>
  <mi>N</mi>
  <mi>O</mi>
  <mi>P</mi>
  <mi>Q</mi>
  <mi>R</mi>
  <mi>S</mi>
  <mi>T</mi>
  <mi>U</mi>
  <mi>V</mi>
  <mi>W</mi>
  <mi>X</mi>
  <mi>Y</mi>
  <mi>Z</mi>
  <mspace width="0.333em"/>
  <mi>a</mi>
  <mi>b</mi>
  <mi>c</mi>
  <mi>d</mi>
  <mi>e</mi>
  <mi>f</mi>
  <mi>g</mi>
  <mi>h</mi>
  <mi>i</mi>
  <mi>j</mi>
  <mi>k</mi>
  <mi>l</mi>
  <mi>m</mi>
  <mi>n</mi>
  <mi>o</mi>
  <mi>p</mi>
  <mi>q</mi>
  <mi>r</mi>
  <mi>s</mi>
  <mi>t</mi>
  <mi>u</mi>
  <mi>v</mi>
  <mi>w</mi>
  <mi>x</mi>
  <mi>y</mi>
  <mi>z</mi>
  <mspace width="0.333em"/>
  <mi>ı</mi>
  <mi>𝚥</mi>
</mrow>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi>Γ</mi>
  <mi>Δ</mi>
  <mi>Θ</mi>
  <mi>Λ</mi>
  <mi>Ξ</mi>
  <mi>Π</mi>
  <mi>Σ</mi>
  <mi>Υ</mi>
  <mi>Φ</mi>
  <mi>Ψ</mi>
  <mi>Ω</mi>
  <mspace width="0.333em"/>
  <mi>α</mi>
  <mi>β</mi>
  <mi>γ</mi>
  <mi>δ</mi>
  <mi>ε</mi>
  <mi>ζ</mi>
  <mi>η</mi>
  <mi>θ</mi>
  <mi>ι</mi>
  <mi>κ</mi>
  <mi>λ</mi>
  <mi>μ</mi>
  <mi>ν</mi>
  <mi>ξ</mi>
  <mi>π</mi>
  <mi>ρ</mi>
  <mi>ς</mi>
  <mi>σ</mi>
  <mi>τ</mi>
  <mi>υ</mi>
  <mi>φ</mi>
  <mi>χ</mi>
  <mi>ψ</mi>
  <mi>ω</mi>
  <mspace width="0.333em"/>
  <mi>ϵ</mi>
  <mi>ϑ</mi>
  <mi>ϕ</mi>
  <mi>ϰ</mi>
  <mi>ϱ</mi>
  <mi>ϖ</mi>
  <mspace width="0.333em"/>
  <mi mathvariant="normal">∂</mi>
  <mo>∇</mo>
</mrow>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mn mathvariant="italic">0123456789</mn>
</math> <a class="brackets" href="#italic-digits" id="footnote-reference-4" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a></p>
</dd>
<dt>mathbfit:</dt>
<dd><p><span class="math problematic m">\mathbfit{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</span>
<span class="math problematic m">\mathbfit{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖ\ \partial∇}</span></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 398)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\mathbfit&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 398)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\mathbfit&quot;</p>
</aside>
</dd>
<dt>mathcal:</dt>
<dd><p><span class="math problematic m">\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</span></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 401)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">The symbol &quot;a&quot; is not available in the font &quot;cal&quot;</p>
</aside>
</dd>
<dt>mathscr:</dt>
<dd><p><span class="math problematic m">\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</span></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 403)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\mathscr&quot;</p>
</aside>
</dd>
<dt>mathbb:</dt>
<dd><p><span class="math problematic m">\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</span>
<span class="math problematic m">\mathbb{ΓΠΣ\ γπ}</span>
<span class="math problematic m">\mathbb{0123456789}</span></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 405)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">The symbol &quot;a&quot; is not available in the font &quot;bb&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 405)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">The symbol &quot;\Gamma&quot; is not available in the font &quot;bb&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 405)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">The symbol &quot;0&quot; is not available in the font &quot;bb&quot;</p>
</aside>
</dd>
<dt>mathfrak:</dt>
<dd><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi mathvariant="fraktur">A</mi>
  <mi mathvariant="fraktur">B</mi>
  <mi mathvariant="fraktur">C</mi>
  <mi mathvariant="fraktur">D</mi>
  <mi mathvariant="fraktur">E</mi>
  <mi mathvariant="fraktur">F</mi>
  <mi mathvariant="fraktur">G</mi>
  <mi mathvariant="fraktur">H</mi>
  <mi mathvariant="fraktur">I</mi>
  <mi mathvariant="fraktur">J</mi>
  <mi mathvariant="fraktur">K</mi>
  <mi mathvariant="fraktur">L</mi>
  <mi mathvariant="fraktur">M</mi>
  <mi mathvariant="fraktur">N</mi>
  <mi mathvariant="fraktur">O</mi>
  <mi mathvariant="fraktur">P</mi>
  <mi mathvariant="fraktur">Q</mi>
  <mi mathvariant="fraktur">R</mi>
  <mi mathvariant="fraktur">S</mi>
  <mi mathvariant="fraktur">T</mi>
  <mi mathvariant="fraktur">U</mi>
  <mi mathvariant="fraktur">V</mi>
  <mi mathvariant="fraktur">W</mi>
  <mi mathvariant="fraktur">X</mi>
  <mi mathvariant="fraktur">Y</mi>
  <mi mathvariant="fraktur">Z</mi>
  <mspace width="0.333em"/>
  <mi mathvariant="fraktur">a</mi>
  <mi mathvariant="fraktur">b</mi>
  <mi mathvariant="fraktur">c</mi>
  <mi mathvariant="fraktur">d</mi>
  <mi mathvariant="fraktur">e</mi>
  <mi mathvariant="fraktur">f</mi>
  <mi mathvariant="fraktur">g</mi>
  <mi mathvariant="fraktur">h</mi>
  <mi mathvariant="fraktur">i</mi>
  <mi mathvariant="fraktur">j</mi>
  <mi mathvariant="fraktur">k</mi>
  <mi mathvariant="fraktur">l</mi>
  <mi mathvariant="fraktur">m</mi>
  <mi mathvariant="fraktur">n</mi>
  <mi mathvariant="fraktur">o</mi>
  <mi mathvariant="fraktur">p</mi>
  <mi mathvariant="fraktur">q</mi>
  <mi mathvariant="fraktur">r</mi>
  <mi mathvariant="fraktur">s</mi>
  <mi mathvariant="fraktur">t</mi>
  <mi mathvariant="fraktur">u</mi>
  <mi mathvariant="fraktur">v</mi>
  <mi mathvariant="fraktur">w</mi>
  <mi mathvariant="fraktur">x</mi>
  <mi mathvariant="fraktur">y</mi>
  <mi mathvariant="fraktur">z</mi>
</mrow>
</math></p>
</dd>
<dt>mathsf:</dt>
<dd><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi mathvariant="sans-serif">A</mi>
  <mi mathvariant="sans-serif">B</mi>
  <mi mathvariant="sans-serif">C</mi>
  <mi mathvariant="sans-serif">D</mi>
  <mi mathvariant="sans-serif">E</mi>
  <mi mathvariant="sans-serif">F</mi>
  <mi mathvariant="sans-serif">G</mi>
  <mi mathvariant="sans-serif">H</mi>
  <mi mathvariant="sans-serif">I</mi>
  <mi mathvariant="sans-serif">J</mi>
  <mi mathvariant="sans-serif">K</mi>
  <mi mathvariant="sans-serif">L</mi>
  <mi mathvariant="sans-serif">M</mi>
  <mi mathvariant="sans-serif">N</mi>
  <mi mathvariant="sans-serif">O</mi>
  <mi mathvariant="sans-serif">P</mi>
  <mi mathvariant="sans-serif">Q</mi>
  <mi mathvariant="sans-serif">R</mi>
  <mi mathvariant="sans-serif">S</mi>
  <mi mathvariant="sans-serif">T</mi>
  <mi mathvariant="sans-serif">U</mi>
  <mi mathvariant="sans-serif">V</mi>
  <mi mathvariant="sans-serif">W</mi>
  <mi mathvariant="sans-serif">X</mi>
  <mi mathvariant="sans-serif">Y</mi>
  <mi mathvariant="sans-serif">Z</mi>
  <mspace width="0.333em"/>
  <mi mathvariant="sans-serif">a</mi>
  <mi mathvariant="sans-serif">b</mi>
  <mi mathvariant="sans-serif">c</mi>
  <mi mathvariant="sans-serif">d</mi>
  <mi mathvariant="sans-serif">e</mi>
  <mi mathvariant="sans-serif">f</mi>
  <mi mathvariant="sans-serif">g</mi>
  <mi mathvariant="sans-serif">h</mi>
  <mi mathvariant="sans-serif">i</mi>
  <mi mathvariant="sans-serif">j</mi>
  <mi mathvariant="sans-serif">k</mi>
  <mi mathvariant="sans-serif">l</mi>
  <mi mathvariant="sans-serif">m</mi>
  <mi mathvariant="sans-serif">n</mi>
  <mi mathvariant="sans-serif">o</mi>
  <mi mathvariant="sans-serif">p</mi>
  <mi mathvariant="sans-serif">q</mi>
  <mi mathvariant="sans-serif">r</mi>
  <mi mathvariant="sans-serif">s</mi>
  <mi mathvariant="sans-serif">t</mi>
  <mi mathvariant="sans-serif">u</mi>
  <mi mathvariant="sans-serif">v</mi>
  <mi mathvariant="sans-serif">w</mi>
  <mi mathvariant="sans-serif">x</mi>
  <mi mathvariant="sans-serif">y</mi>
  <mi mathvariant="sans-serif">z</mi>
</mrow>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mn mathvariant="sans-serif">0123456789</mn>
</math></p>
</dd>
<dt>mathsfit:</dt>
<dd><p><span class="math problematic m">\mathsfit{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</span></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 414)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\mathsfit&quot;</p>
</aside>
</dd>
<dt>mathsfbfit:</dt>
<dd><p><span class="math problematic m">\mathsfbfit{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}</span>
<span class="math problematic m">\mathsfbfit{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖ\ \partial∇}</span></p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 416)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\mathsfbfit&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 416)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\mathsfbfit&quot;</p>
</aside>
</dd>
<dt>mathtt:</dt>
<dd><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi mathvariant="monospace">A</mi>
  <mi mathvariant="monospace">B</mi>
  <mi mathvariant="monospace">C</mi>
  <mi mathvariant="monospace">D</mi>
  <mi mathvariant="monospace">E</mi>
  <mi mathvariant="monospace">F</mi>
  <mi mathvariant="monospace">G</mi>
  <mi mathvariant="monospace">H</mi>
  <mi mathvariant="monospace">I</mi>
  <mi mathvariant="monospace">J</mi>
  <mi mathvariant="monospace">K</mi>
  <mi mathvariant="monospace">L</mi>
  <mi mathvariant="monospace">M</mi>
  <mi mathvariant="monospace">N</mi>
  <mi mathvariant="monospace">O</mi>
  <mi mathvariant="monospace">P</mi>
  <mi mathvariant="monospace">Q</mi>
  <mi mathvariant="monospace">R</mi>
  <mi mathvariant="monospace">S</mi>
  <mi mathvariant="monospace">T</mi>
  <mi mathvariant="monospace">U</mi>
  <mi mathvariant="monospace">V</mi>
  <mi mathvariant="monospace">W</mi>
  <mi mathvariant="monospace">X</mi>
  <mi mathvariant="monospace">Y</mi>
  <mi mathvariant="monospace">Z</mi>
  <mspace width="0.333em"/>
  <mi mathvariant="monospace">a</mi>
  <mi mathvariant="monospace">b</mi>
  <mi mathvariant="monospace">c</mi>
  <mi mathvariant="monospace">d</mi>
  <mi mathvariant="monospace">e</mi>
  <mi mathvariant="monospace">f</mi>
  <mi mathvariant="monospace">g</mi>
  <mi mathvariant="monospace">h</mi>
  <mi mathvariant="monospace">i</mi>
  <mi mathvariant="monospace">j</mi>
  <mi mathvariant="monospace">k</mi>
  <mi mathvariant="monospace">l</mi>
  <mi mathvariant="monospace">m</mi>
  <mi mathvariant="monospace">n</mi>
  <mi mathvariant="monospace">o</mi>
  <mi mathvariant="monospace">p</mi>
  <mi mathvariant="monospace">q</mi>
  <mi mathvariant="monospace">r</mi>
  <mi mathvariant="monospace">s</mi>
  <mi mathvariant="monospace">t</mi>
  <mi mathvariant="monospace">u</mi>
  <mi mathvariant="monospace">v</mi>
  <mi mathvariant="monospace">w</mi>
  <mi mathvariant="monospace">x</mi>
  <mi mathvariant="monospace">y</mi>
  <mi mathvariant="monospace">z</mi>
</mrow>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mn mathvariant="monospace">0123456789</mn>
</math></p>
</dd>
</dl>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="italic-digits" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
<span class="backrefs">(<a role="doc-backlink" href="#footnote-reference-3">1</a>,<a role="doc-backlink" href="#footnote-reference-4">2</a>)</span>
<p>Italic digits are not defined in Unicode
but work in LaTeX.</p>
</aside>
</aside>
<p>In contrast to the <em>math alphabet</em> selectors, <span class="docutils literal">\boldsymbol</span> only
changes the <em>font weight</em>. It can be used to get a bold version of
any mathematical symbol:</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <msub>
    <mi>V</mi>
    <mi>i</mi>
  </msub>
  <mi>x</mi>
  <mo>±</mo>
  <mi>cos</mi>
  <mo stretchy="false">(</mo>
  <mi>α</mi>
  <mo stretchy="false">)</mo>
  <mo>≈</mo>
  <mn>3</mn>
  <mi mathvariant="normal">Γ</mi>
  <mo lspace="1.000em">∀</mo>
  <mi>x</mi>
  <mo>∈</mo>
  <mi mathvariant="double-struck">R</mi>
</mrow>
</math>
</div>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <msub>
    <mi mathvariant="bold-italic">V</mi>
    <mi mathvariant="bold-italic">i</mi>
  </msub>
  <mi mathvariant="bold-italic">x</mi>
  <mo mathvariant="bold">±</mo>
  <mi mathvariant="bold">cos</mi>
  <mo mathvariant="bold" stretchy="false">(</mo>
  <mi mathvariant="bold-italic">α</mi>
  <mo mathvariant="bold" stretchy="false">)</mo>
  <mo mathvariant="bold">≈</mo>
  <mn mathvariant="bold">3</mn>
  <mi mathvariant="bold">Γ</mi>
  <mo mathvariant="bold" lspace="1.000em">∀</mo>
  <mi mathvariant="bold-italic">x</mi>
  <mo mathvariant="bold">∈</mo>
  <mi mathvariant="double-struck">R</mi>
</mrow>
</math>
</div>
<p>It is usually ill-advised to apply <span class="docutils literal">\boldsymbol</span> to more than one symbol
at a time.</p>
</section>
<section id="miscellaneous-symbols">
<h3><a class="toc-backref" href="#toc-entry-13" role="doc-backlink"><span class="sectnum">2.9 </span>Miscellaneous symbols</a></h3>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>#</mo>
</math></p></td>
<td><p><span class="docutils literal">\#</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>♣</mo>
</math></p></td>
<td><p><span class="docutils literal">\clubsuit</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>¬</mo>
</math></p></td>
<td><p><span class="docutils literal">\neg</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>&amp;</mo>
</math></p></td>
<td><p><span class="docutils literal">\&amp;</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>♦</mo>
</math></p></td>
<td><p><span class="docutils literal">\diamondsuit</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∄</mo>
</math></p></td>
<td><p><span class="docutils literal">\nexists</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∠</mo>
</math></p></td>
<td><p><span class="docutils literal">\angle</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">∅</mi>
</math></p></td>
<td><p><span class="docutils literal">\emptyset</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>′</mo>
</math></p></td>
<td><p><span class="docutils literal">\prime</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>‵</mo>
</math></p></td>
<td><p><span class="docutils literal">\backprime</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∃</mo>
</math></p></td>
<td><p><span class="docutils literal">\exists</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>♯</mo>
</math></p></td>
<td><p><span class="docutils literal">\sharp</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>★</mo>
</math></p></td>
<td><p><span class="docutils literal">\bigstar</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>♭</mo>
</math></p></td>
<td><p><span class="docutils literal">\flat</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>♠</mo>
</math></p></td>
<td><p><span class="docutils literal">\spadesuit</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⧫</mo>
</math></p></td>
<td><p><span class="docutils literal">\blacklozenge</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∀</mo>
</math></p></td>
<td><p><span class="docutils literal">\forall</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∢</mo>
</math></p></td>
<td><p><span class="docutils literal">\sphericalangle</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>◼</mo>
</math></p></td>
<td><p><span class="docutils literal">\blacksquare</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>♥</mo>
</math></p></td>
<td><p><span class="docutils literal">\heartsuit</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>□</mo>
</math></p></td>
<td><p><span class="docutils literal">\square</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>▴</mo>
</math></p></td>
<td><p><span class="docutils literal">\blacktriangle</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">∞</mi>
</math></p></td>
<td><p><span class="docutils literal">\infty</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>√</mo>
</math></p></td>
<td><p><span class="docutils literal">\surd</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>▾</mo>
</math></p></td>
<td><p><span class="docutils literal">\blacktriangledown</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>◊</mo>
</math></p></td>
<td><p><span class="docutils literal">\lozenge</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊤</mo>
</math></p></td>
<td><p><span class="docutils literal">\top</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊥</mo>
</math></p></td>
<td><p><span class="docutils literal">\bot</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∡</mo>
</math></p></td>
<td><p><span class="docutils literal">\measuredangle</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>△</mo>
</math></p></td>
<td><p><span class="docutils literal">\triangle</span></p></td>
</tr>
<tr><td><p><span class="math problematic m">\diagdown</span></p></td>
<td><p><span class="docutils literal">\diagdown</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∇</mo>
</math></p></td>
<td><p><span class="docutils literal">\nabla</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>▿</mo>
</math></p></td>
<td><p><span class="docutils literal">\triangledown</span></p></td>
</tr>
<tr><td><p><span class="math problematic m">\diagup</span></p></td>
<td><p><span class="docutils literal">\diagup</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>♮</mo>
</math></p></td>
<td><p><span class="docutils literal">\natural</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">Ø</mi>
</math></p></td>
<td><p><span class="docutils literal">\varnothing</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 461)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\diagdown&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 462)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\diagup&quot;</p>
</aside>
</section>
<section id="punctuation">
<h3><a class="toc-backref" href="#toc-entry-14" role="doc-backlink"><span class="sectnum">2.10 </span>Punctuation</a></h3>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>.</mo>
</math></p></td>
<td><p><span class="docutils literal">.</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>!</mo>
</math></p></td>
<td><p><span class="docutils literal">!</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋮</mo>
</math></p></td>
<td><p><span class="docutils literal">\vdots</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">/</mo>
</math></p></td>
<td><p><span class="docutils literal">/</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>?</mo>
</math></p></td>
<td><p><span class="docutils literal">?</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋯</mo>
</math></p></td>
<td><p><span class="docutils literal">\dotsb</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">|</mo>
</math></p></td>
<td><p><span class="docutils literal">|</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo lspace="0.111em" rspace="0.333em">:</mo>
</math></p></td>
<td><p><span class="docutils literal">\colon</span> <a class="brackets" href="#footnote-1" id="footnote-reference-5" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a></p></td>
<td><p><span class="math problematic m">\dotsc</span></p></td>
<td><p><span class="docutils literal">\dotsc</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msup>
  <mrow/>
  <mo>′</mo>
</msup>
</math></p></td>
<td><p><span class="docutils literal">'</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋯</mo>
</math></p></td>
<td><p><span class="docutils literal">\cdots</span></p></td>
<td><p><span class="math problematic m">\dotsi</span></p></td>
<td><p><span class="docutils literal">\dotsi</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>;</mo>
</math></p></td>
<td><p><span class="docutils literal">;</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋱</mo>
</math></p></td>
<td><p><span class="docutils literal">\ddots</span></p></td>
<td><p><span class="math problematic m">\dotsm</span></p></td>
<td><p><span class="docutils literal">\dotsm</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>:</mo>
</math></p></td>
<td><p><span class="docutils literal">:</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>…</mo>
</math></p></td>
<td><p><span class="docutils literal">\ldots</span></p></td>
<td><p><span class="math problematic m">\dotso</span></p></td>
<td><p><span class="docutils literal">\dotso</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 473)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\dotsc&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 474)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\dotsi&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 475)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\dotsm&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 476)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\dotso&quot;</p>
</aside>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="footnote-1" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-5">3</a><span class="fn-bracket">]</span></span>
<p>Punctuation (not ratio):
Compare spacing in <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi>a</mi>
  <mo lspace="0.111em" rspace="0.333em">:</mo>
  <mi>b</mi>
  <mo>→</mo>
  <mi>c</mi>
</mrow>
</math> to <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi>a</mi>
  <mo>:</mo>
  <mi>b</mi>
  <mo>=</mo>
  <mi>c</mi>
</mrow>
</math>.</p>
</aside>
</aside>
</section>
<section id="relation-symbols">
<h3><a class="toc-backref" href="#toc-entry-15" role="doc-backlink"><span class="sectnum">2.11 </span>Relation symbols</a></h3>
<section id="arrows">
<h4><a class="toc-backref" href="#toc-entry-16" role="doc-backlink"><span class="sectnum">2.11.1 </span>Arrows</a></h4>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↺</mo>
</math></p></td>
<td><p><span class="docutils literal">\circlearrowleft</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↻</mo>
</math></p></td>
<td><p><span class="docutils literal">\circlearrowright</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↶</mo>
</math></p></td>
<td><p><span class="docutils literal">\curvearrowleft</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↷</mo>
</math></p></td>
<td><p><span class="docutils literal">\curvearrowright</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↩</mo>
</math></p></td>
<td><p><span class="docutils literal">\hookleftarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↪</mo>
</math></p></td>
<td><p><span class="docutils literal">\hookrightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>←</mo>
</math></p></td>
<td><p><span class="docutils literal">\leftarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>→</mo>
</math></p></td>
<td><p><span class="docutils literal">\rightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇐</mo>
</math></p></td>
<td><p><span class="docutils literal">\Leftarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇒</mo>
</math></p></td>
<td><p><span class="docutils literal">\Rightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↢</mo>
</math></p></td>
<td><p><span class="docutils literal">\leftarrowtail</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↣</mo>
</math></p></td>
<td><p><span class="docutils literal">\rightarrowtail</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↽</mo>
</math></p></td>
<td><p><span class="docutils literal">\leftharpoondown</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇁</mo>
</math></p></td>
<td><p><span class="docutils literal">\rightharpoondown</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↼</mo>
</math></p></td>
<td><p><span class="docutils literal">\leftharpoonup</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇀</mo>
</math></p></td>
<td><p><span class="docutils literal">\rightharpoonup</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇇</mo>
</math></p></td>
<td><p><span class="docutils literal">\leftleftarrows</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇉</mo>
</math></p></td>
<td><p><span class="docutils literal">\rightrightarrows</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↔</mo>
</math></p></td>
<td><p><span class="docutils literal">\leftrightarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇔</mo>
</math></p></td>
<td><p><span class="docutils literal">\Leftrightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇆</mo>
</math></p></td>
<td><p><span class="docutils literal">\leftrightarrows</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇄</mo>
</math></p></td>
<td><p><span class="docutils literal">\rightleftarrows</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇋</mo>
</math></p></td>
<td><p><span class="docutils literal">\leftrightharpoons</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇌</mo>
</math></p></td>
<td><p><span class="docutils literal">\rightleftharpoons</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↭</mo>
</math></p></td>
<td><p><span class="docutils literal">\leftrightsquigarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↝</mo>
</math></p></td>
<td><p><span class="docutils literal">\rightsquigarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇚</mo>
</math></p></td>
<td><p><span class="docutils literal">\Lleftarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇛</mo>
</math></p></td>
<td><p><span class="docutils literal">\Rrightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>←</mo>
</math></p></td>
<td><p><span class="docutils literal">\longleftarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>→</mo>
</math></p></td>
<td><p><span class="docutils literal">\longrightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇐</mo>
</math></p></td>
<td><p><span class="docutils literal">\Longleftarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇒</mo>
</math></p></td>
<td><p><span class="docutils literal">\Longrightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↔</mo>
</math></p></td>
<td><p><span class="docutils literal">\longleftrightarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇔</mo>
</math></p></td>
<td><p><span class="docutils literal">\Longleftrightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↫</mo>
</math></p></td>
<td><p><span class="docutils literal">\looparrowleft</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↬</mo>
</math></p></td>
<td><p><span class="docutils literal">\looparrowright</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↰</mo>
</math></p></td>
<td><p><span class="docutils literal">\Lsh</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↱</mo>
</math></p></td>
<td><p><span class="docutils literal">\Rsh</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↦</mo>
</math></p></td>
<td><p><span class="docutils literal">\mapsto</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↦</mo>
</math></p></td>
<td><p><span class="docutils literal">\longmapsto</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊸</mo>
</math></p></td>
<td><p><span class="docutils literal">\multimap</span></p></td>
<td></td>
<td></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↚</mo>
</math></p></td>
<td><p><span class="docutils literal">\nleftarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↛</mo>
</math></p></td>
<td><p><span class="docutils literal">\nrightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇍</mo>
</math></p></td>
<td><p><span class="docutils literal">\nLeftarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇏</mo>
</math></p></td>
<td><p><span class="docutils literal">\nRightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↮</mo>
</math></p></td>
<td><p><span class="docutils literal">\nleftrightarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇎</mo>
</math></p></td>
<td><p><span class="docutils literal">\nLeftrightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↖</mo>
</math></p></td>
<td><p><span class="docutils literal">\nwarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↗</mo>
</math></p></td>
<td><p><span class="docutils literal">\nearrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↙</mo>
</math></p></td>
<td><p><span class="docutils literal">\swarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↘</mo>
</math></p></td>
<td><p><span class="docutils literal">\searrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↞</mo>
</math></p></td>
<td><p><span class="docutils literal">\twoheadleftarrow</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↠</mo>
</math></p></td>
<td><p><span class="docutils literal">\twoheadrightarrow</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↿</mo>
</math></p></td>
<td><p><span class="docutils literal">\upharpoonleft</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↾</mo>
</math></p></td>
<td><p><span class="docutils literal">\upharpoonright</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇃</mo>
</math></p></td>
<td><p><span class="docutils literal">\downharpoonleft</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇂</mo>
</math></p></td>
<td><p><span class="docutils literal">\downharpoonright</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇈</mo>
</math></p></td>
<td><p><span class="docutils literal">\upuparrows</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⇊</mo>
</math></p></td>
<td><p><span class="docutils literal">\downdownarrows</span></p></td>
</tr>
</tbody>
</table>
<p>Synonyms: <math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>←</mo>
</math> <span class="docutils literal">\gets</span>, <math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>→</mo>
</math> <span class="docutils literal">\to</span>, <math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>↾</mo>
</math> <span class="docutils literal">\restriction</span>.</p>
</section>
<section id="comparison">
<h4><a class="toc-backref" href="#toc-entry-17" role="doc-backlink"><span class="sectnum">2.11.2 </span>Comparison</a></h4>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>&lt;</mo>
</math></p></td>
<td><p><span class="docutils literal">&lt;</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≥</mo>
</math></p></td>
<td><p><span class="docutils literal">\geq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≪</mo>
</math></p></td>
<td><p><span class="docutils literal">\ll</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≺</mo>
</math></p></td>
<td><p><span class="docutils literal">\prec</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>=</mo>
</math></p></td>
<td><p><span class="docutils literal">=</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≧</mo>
</math></p></td>
<td><p><span class="docutils literal">\geqq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋘</mo>
</math></p></td>
<td><p><span class="docutils literal">\lll</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪷</mo>
</math></p></td>
<td><p><span class="docutils literal">\precapprox</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>&gt;</mo>
</math></p></td>
<td><p><span class="docutils literal">&gt;</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⩾</mo>
</math></p></td>
<td><p><span class="docutils literal">\geqslant</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪉</mo>
</math></p></td>
<td><p><span class="docutils literal">\lnapprox</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≼</mo>
</math></p></td>
<td><p><span class="docutils literal">\preccurlyeq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≈</mo>
</math></p></td>
<td><p><span class="docutils literal">\approx</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≫</mo>
</math></p></td>
<td><p><span class="docutils literal">\gg</span></p></td>
<td><p><span class="math problematic m">\lneq</span></p></td>
<td><p><span class="docutils literal">\lneq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪯</mo>
</math></p></td>
<td><p><span class="docutils literal">\preceq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≊</mo>
</math></p></td>
<td><p><span class="docutils literal">\approxeq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋙</mo>
</math></p></td>
<td><p><span class="docutils literal">\ggg</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≨</mo>
</math></p></td>
<td><p><span class="docutils literal">\lneqq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪹</mo>
</math></p></td>
<td><p><span class="docutils literal">\precnapprox</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≈</mo>
</math></p></td>
<td><p><span class="docutils literal">\asymp</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪊</mo>
</math></p></td>
<td><p><span class="docutils literal">\gnapprox</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋦</mo>
</math></p></td>
<td><p><span class="docutils literal">\lnsim</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪵</mo>
</math></p></td>
<td><p><span class="docutils literal">\precneqq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∽</mo>
</math></p></td>
<td><p><span class="docutils literal">\backsim</span></p></td>
<td><p><span class="math problematic m">\gneq</span></p></td>
<td><p><span class="docutils literal">\gneq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≇</mo>
</math></p></td>
<td><p><span class="docutils literal">\ncong</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋨</mo>
</math></p></td>
<td><p><span class="docutils literal">\precnsim</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋍</mo>
</math></p></td>
<td><p><span class="docutils literal">\backsimeq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≩</mo>
</math></p></td>
<td><p><span class="docutils literal">\gneqq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≠</mo>
</math></p></td>
<td><p><span class="docutils literal">\neq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≾</mo>
</math></p></td>
<td><p><span class="docutils literal">\precsim</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≏</mo>
</math></p></td>
<td><p><span class="docutils literal">\bumpeq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋧</mo>
</math></p></td>
<td><p><span class="docutils literal">\gnsim</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≱</mo>
</math></p></td>
<td><p><span class="docutils literal">\ngeq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≓</mo>
</math></p></td>
<td><p><span class="docutils literal">\risingdotseq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≎</mo>
</math></p></td>
<td><p><span class="docutils literal">\Bumpeq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪆</mo>
</math></p></td>
<td><p><span class="docutils literal">\gtrapprox</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≧̸</mo>
</math></p></td>
<td><p><span class="docutils literal">\ngeqq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∼</mo>
</math></p></td>
<td><p><span class="docutils literal">\sim</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≗</mo>
</math></p></td>
<td><p><span class="docutils literal">\circeq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋛</mo>
</math></p></td>
<td><p><span class="docutils literal">\gtreqless</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⩾̸</mo>
</math></p></td>
<td><p><span class="docutils literal">\ngeqslant</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≃</mo>
</math></p></td>
<td><p><span class="docutils literal">\simeq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≅</mo>
</math></p></td>
<td><p><span class="docutils literal">\cong</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪌</mo>
</math></p></td>
<td><p><span class="docutils literal">\gtreqqless</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≯</mo>
</math></p></td>
<td><p><span class="docutils literal">\ngtr</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≻</mo>
</math></p></td>
<td><p><span class="docutils literal">\succ</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋞</mo>
</math></p></td>
<td><p><span class="docutils literal">\curlyeqprec</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≷</mo>
</math></p></td>
<td><p><span class="docutils literal">\gtrless</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≰</mo>
</math></p></td>
<td><p><span class="docutils literal">\nleq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪸</mo>
</math></p></td>
<td><p><span class="docutils literal">\succapprox</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋟</mo>
</math></p></td>
<td><p><span class="docutils literal">\curlyeqsucc</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≳</mo>
</math></p></td>
<td><p><span class="docutils literal">\gtrsim</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≦̸</mo>
</math></p></td>
<td><p><span class="docutils literal">\nleqq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≽</mo>
</math></p></td>
<td><p><span class="docutils literal">\succcurlyeq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≐</mo>
</math></p></td>
<td><p><span class="docutils literal">\doteq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≤</mo>
</math></p></td>
<td><p><span class="docutils literal">\leq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⩽̸</mo>
</math></p></td>
<td><p><span class="docutils literal">\nleqslant</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪰</mo>
</math></p></td>
<td><p><span class="docutils literal">\succeq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≑</mo>
</math></p></td>
<td><p><span class="docutils literal">\doteqdot</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≦</mo>
</math></p></td>
<td><p><span class="docutils literal">\leqq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≮</mo>
</math></p></td>
<td><p><span class="docutils literal">\nless</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪺</mo>
</math></p></td>
<td><p><span class="docutils literal">\succnapprox</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≖</mo>
</math></p></td>
<td><p><span class="docutils literal">\eqcirc</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⩽</mo>
</math></p></td>
<td><p><span class="docutils literal">\leqslant</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊀</mo>
</math></p></td>
<td><p><span class="docutils literal">\nprec</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪶</mo>
</math></p></td>
<td><p><span class="docutils literal">\succneqq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≂</mo>
</math></p></td>
<td><p><span class="docutils literal">\eqsim</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪅</mo>
</math></p></td>
<td><p><span class="docutils literal">\lessapprox</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪯̸</mo>
</math></p></td>
<td><p><span class="docutils literal">\npreceq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋩</mo>
</math></p></td>
<td><p><span class="docutils literal">\succnsim</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪖</mo>
</math></p></td>
<td><p><span class="docutils literal">\eqslantgtr</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋚</mo>
</math></p></td>
<td><p><span class="docutils literal">\lesseqgtr</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≁</mo>
</math></p></td>
<td><p><span class="docutils literal">\nsim</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≿</mo>
</math></p></td>
<td><p><span class="docutils literal">\succsim</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪕</mo>
</math></p></td>
<td><p><span class="docutils literal">\eqslantless</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪋</mo>
</math></p></td>
<td><p><span class="docutils literal">\lesseqqgtr</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊁</mo>
</math></p></td>
<td><p><span class="docutils literal">\nsucc</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≈</mo>
</math></p></td>
<td><p><span class="docutils literal">\thickapprox</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≡</mo>
</math></p></td>
<td><p><span class="docutils literal">\equiv</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≶</mo>
</math></p></td>
<td><p><span class="docutils literal">\lessgtr</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⪰̸</mo>
</math></p></td>
<td><p><span class="docutils literal">\nsucceq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∼</mo>
</math></p></td>
<td><p><span class="docutils literal">\thicksim</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≒</mo>
</math></p></td>
<td><p><span class="docutils literal">\fallingdotseq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≲</mo>
</math></p></td>
<td><p><span class="docutils literal">\lesssim</span></p></td>
<td></td>
<td></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≜</mo>
</math></p></td>
<td><p><span class="docutils literal">\triangleq</span></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 534)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\lneq&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 537)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\gneq&quot;</p>
</aside>
<p>The commands <span class="docutils literal">\lvertneqq</span> and <span class="docutils literal">\gvertneqq</span> are not supported
with MathML output, as there is no corresponding Unicode character.</p>
<p>Synonyms: <math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≠</mo>
</math> <span class="docutils literal">\ne</span>, <math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≤</mo>
</math> <span class="docutils literal">\le</span>, <math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≥</mo>
</math> <span class="docutils literal">\ge</span>,
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≑</mo>
</math> <span class="docutils literal">\Doteq</span>, <math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋘</mo>
</math> <span class="docutils literal">\llless</span>, <math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋙</mo>
</math> <span class="docutils literal">\gggtr</span>.</p>
<p>Symbols can be negated prepending <span class="docutils literal">\not</span>, e.g.
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≠</mo>
</math> <span class="docutils literal">\not=</span>, <math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≢</mo>
</math> <span class="docutils literal">\not\equiv</span>,
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mpadded width="0">
    <mspace width="0.1em"/>
    <mo>/</mo>
  </mpadded>
  <mo>≷</mo>
</mrow>
</math> <span class="docutils literal">\not\gtrless</span>, <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mpadded width="0">
    <mspace width="0.1em"/>
    <mo>/</mo>
  </mpadded>
  <mo>≶</mo>
</mrow>
</math> <span class="docutils literal">\not\lessgtr</span>.</p>
</section>
<section id="miscellaneous-relations">
<h4><a class="toc-backref" href="#toc-entry-18" role="doc-backlink"><span class="sectnum">2.11.3 </span>Miscellaneous relations</a></h4>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>϶</mo>
</math></p></td>
<td><p><span class="docutils literal">\backepsilon</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋬</mo>
</math></p></td>
<td><p><span class="docutils literal">\ntrianglelefteq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊆</mo>
</math></p></td>
<td><p><span class="docutils literal">\subseteq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∵</mo>
</math></p></td>
<td><p><span class="docutils literal">\because</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋫</mo>
</math></p></td>
<td><p><span class="docutils literal">\ntriangleright</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⫅</mo>
</math></p></td>
<td><p><span class="docutils literal">\subseteqq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>≬</mo>
</math></p></td>
<td><p><span class="docutils literal">\between</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋭</mo>
</math></p></td>
<td><p><span class="docutils literal">\ntrianglerighteq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊊</mo>
</math></p></td>
<td><p><span class="docutils literal">\subsetneq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>◀</mo>
</math></p></td>
<td><p><span class="docutils literal">\blacktriangleleft</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊬</mo>
</math></p></td>
<td><p><span class="docutils literal">\nvdash</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⫋</mo>
</math></p></td>
<td><p><span class="docutils literal">\subsetneqq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>▶</mo>
</math></p></td>
<td><p><span class="docutils literal">\blacktriangleright</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊮</mo>
</math></p></td>
<td><p><span class="docutils literal">\nVdash</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊃</mo>
</math></p></td>
<td><p><span class="docutils literal">\supset</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋈</mo>
</math></p></td>
<td><p><span class="docutils literal">\bowtie</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊭</mo>
</math></p></td>
<td><p><span class="docutils literal">\nvDash</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋑</mo>
</math></p></td>
<td><p><span class="docutils literal">\Supset</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊣</mo>
</math></p></td>
<td><p><span class="docutils literal">\dashv</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊯</mo>
</math></p></td>
<td><p><span class="docutils literal">\nVDash</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊇</mo>
</math></p></td>
<td><p><span class="docutils literal">\supseteq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⌢</mo>
</math></p></td>
<td><p><span class="docutils literal">\frown</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∥</mo>
</math></p></td>
<td><p><span class="docutils literal">\parallel</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⫆</mo>
</math></p></td>
<td><p><span class="docutils literal">\supseteqq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∈</mo>
</math></p></td>
<td><p><span class="docutils literal">\in</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊥</mo>
</math></p></td>
<td><p><span class="docutils literal">\perp</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊋</mo>
</math></p></td>
<td><p><span class="docutils literal">\supsetneq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">|</mo>
</math></p></td>
<td><p><span class="docutils literal">\mid</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋔</mo>
</math></p></td>
<td><p><span class="docutils literal">\pitchfork</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⫌</mo>
</math></p></td>
<td><p><span class="docutils literal">\supsetneqq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊧</mo>
</math></p></td>
<td><p><span class="docutils literal">\models</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∝</mo>
</math></p></td>
<td><p><span class="docutils literal">\propto</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∴</mo>
</math></p></td>
<td><p><span class="docutils literal">\therefore</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∋</mo>
</math></p></td>
<td><p><span class="docutils literal">\ni</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∣</mo>
</math></p></td>
<td><p><span class="docutils literal">\shortmid</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊴</mo>
</math></p></td>
<td><p><span class="docutils literal">\trianglelefteq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∤</mo>
</math></p></td>
<td><p><span class="docutils literal">\nmid</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∥</mo>
</math></p></td>
<td><p><span class="docutils literal">\shortparallel</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊵</mo>
</math></p></td>
<td><p><span class="docutils literal">\trianglerighteq</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∉</mo>
</math></p></td>
<td><p><span class="docutils literal">\notin</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⌢</mo>
</math></p></td>
<td><p><span class="docutils literal">\smallfrown</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∝</mo>
</math></p></td>
<td><p><span class="docutils literal">\varpropto</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∦</mo>
</math></p></td>
<td><p><span class="docutils literal">\nparallel</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⌣</mo>
</math></p></td>
<td><p><span class="docutils literal">\smallsmile</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>▵</mo>
</math></p></td>
<td><p><span class="docutils literal">\vartriangle</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∤</mo>
</math></p></td>
<td><p><span class="docutils literal">\nshortmid</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⌣</mo>
</math></p></td>
<td><p><span class="docutils literal">\smile</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊲</mo>
</math></p></td>
<td><p><span class="docutils literal">\vartriangleleft</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∦</mo>
</math></p></td>
<td><p><span class="docutils literal">\nshortparallel</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊏</mo>
</math></p></td>
<td><p><span class="docutils literal">\sqsubset</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊳</mo>
</math></p></td>
<td><p><span class="docutils literal">\vartriangleright</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊈</mo>
</math></p></td>
<td><p><span class="docutils literal">\nsubseteq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊑</mo>
</math></p></td>
<td><p><span class="docutils literal">\sqsubseteq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊢</mo>
</math></p></td>
<td><p><span class="docutils literal">\vdash</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⫅̸</mo>
</math></p></td>
<td><p><span class="docutils literal">\nsubseteqq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊐</mo>
</math></p></td>
<td><p><span class="docutils literal">\sqsupset</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊩</mo>
</math></p></td>
<td><p><span class="docutils literal">\Vdash</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊉</mo>
</math></p></td>
<td><p><span class="docutils literal">\nsupseteq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊒</mo>
</math></p></td>
<td><p><span class="docutils literal">\sqsupseteq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊨</mo>
</math></p></td>
<td><p><span class="docutils literal">\vDash</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⫆̸</mo>
</math></p></td>
<td><p><span class="docutils literal">\nsupseteqq</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊂</mo>
</math></p></td>
<td><p><span class="docutils literal">\subset</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⊪</mo>
</math></p></td>
<td><p><span class="docutils literal">\Vvdash</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋪</mo>
</math></p></td>
<td><p><span class="docutils literal">\ntriangleleft</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋐</mo>
</math></p></td>
<td><p><span class="docutils literal">\Subset</span></p></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<p>Synonyms: <span class="math problematic m">\owns</span> <span class="docutils literal">\owns</span>.</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 594)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\owns&quot;</p>
</aside>
<p>Symbols can be negated prepending <span class="docutils literal">\not</span>, e.g.
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∉</mo>
</math> <span class="docutils literal">\not\in</span>, <math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>∌</mo>
</math> <span class="docutils literal">\not\ni</span>.</p>
<p>The commands <span class="docutils literal">\varsubsetneq</span>, <span class="docutils literal">\varsubsetneqq</span>, <span class="docutils literal">\varsupsetneq</span>,
and <span class="docutils literal">\varsupsetneqq</span> are not supported with MathML output as there is no
corresponding Unicode character.</p>
</section>
</section>
<section id="variable-sized-operators">
<h3><a class="toc-backref" href="#toc-entry-19" role="doc-backlink"><span class="sectnum">2.12 </span>Variable-sized operators</a></h3>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">∑</mo>
</math>      <span class="docutils literal">\sum</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">∏</mo>
</math>     <span class="docutils literal">\prod</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">⋂</mo>
</math>   <span class="docutils literal">\bigcap</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">⨀</mo>
</math>   <span class="docutils literal">\bigodot</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">∫</mo>
</math>      <span class="docutils literal">\int</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">∐</mo>
</math>   <span class="docutils literal">\coprod</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo>⋃</mo>
</math>   <span class="docutils literal">\bigcup</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">⨁</mo>
</math>  <span class="docutils literal">\bigoplus</span></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">∮</mo>
</math>     <span class="docutils literal">\oint</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">⋀</mo>
</math> <span class="docutils literal">\bigwedge</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">⨄</mo>
</math> <span class="docutils literal">\biguplus</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">⨂</mo>
</math> <span class="docutils literal">\bigotimes</span></p></td>
</tr>
<tr><td><p><span class="math problematic m">\smallint</span> <span class="docutils literal">\smallint</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">⋁</mo>
</math>   <span class="docutils literal">\bigvee</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mo stretchy="false">⨆</mo>
</math> <span class="docutils literal">\bigsqcup</span></p></td>
<td></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 612)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\smallint&quot;</p>
</aside>
<p>Larger symbols are used in displayed formulas, sum-like symbols have
indices above/below the symbol:</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <msubsup>
    <mo stretchy="false">∑</mo>
    <mrow>
      <mi>n</mi>
      <mo>=</mo>
      <mn>1</mn>
    </mrow>
    <mi>N</mi>
  </msubsup>
  <msub>
    <mi>a</mi>
    <mi>n</mi>
  </msub>
  <msubsup>
    <mo lspace="2.167em" stretchy="false">∫</mo>
    <mn>0</mn>
    <mn>1</mn>
  </msubsup>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo rspace="0.167em" stretchy="false">)</mo>
  <mi>d</mi>
  <mi>x</mi>
  <msubsup>
    <mo lspace="2.167em" stretchy="false">∏</mo>
    <mrow>
      <mi>i</mi>
      <mo>=</mo>
      <mn>1</mn>
    </mrow>
    <mn>10</mn>
  </msubsup>
  <msub>
    <mi>b</mi>
    <mi>i</mi>
  </msub>
  <mo>…</mo>
</mrow>
</math>
</div>
</section>
</section>
<section id="notations">
<h2><a class="toc-backref" href="#toc-entry-20" role="doc-backlink"><span class="sectnum">3 </span>Notations</a></h2>
<section id="top-and-bottom-embellishments">
<h3><a class="toc-backref" href="#toc-entry-21" role="doc-backlink"><span class="sectnum">3.1 </span>Top and bottom embellishments</a></h3>
<p>See <a class="reference internal" href="#accents-and-embellishments">Accents and embellishments</a>.</p>
</section>
<section id="extensible-arrows">
<h3><a class="toc-backref" href="#toc-entry-22" role="doc-backlink"><span class="sectnum">3.2 </span>Extensible arrows</a></h3>
<p>xleftarrow and xrightarrow produce arrows that extend automatically to
accommodate unusually wide subscripts or superscripts. These commands
take one optional argument (the subscript) and one mandatory argument
(the superscript, possibly empty):</p>
<pre class="literal-block">A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C</pre>
<p>results in</p>
<pre class="math problematic m">
A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 644)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\xleftarrow&quot;</p>
</aside>
</section>
<section id="affixing-symbols-to-other-symbols">
<h3><a class="toc-backref" href="#toc-entry-23" role="doc-backlink"><span class="sectnum">3.3 </span>Affixing symbols to other symbols</a></h3>
<p>In addition to the standard <a class="reference internal" href="#accents-and-embellishments">accents and embellishments</a>, other symbols
can be placed above or below a base symbol with the <span class="docutils literal">\overset</span> and
<span class="docutils literal">\underset</span> commands. The symbol is set in &quot;scriptstyle&quot; (smaller font
size). For example, writing <span class="docutils literal"><span class="pre">\overset{*}{X}</span></span> becomes <math xmlns="http://www.w3.org/1998/Math/MathML">
<mover>
  <mi>X</mi>
  <mo>*</mo>
</mover>
</math>
and <span class="docutils literal"><span class="pre">\underset{+}{M}</span></span> becomes <math xmlns="http://www.w3.org/1998/Math/MathML">
<munder>
  <mi>M</mi>
  <mo>+</mo>
</munder>
</math>.</p>
</section>
<section id="matrices">
<h3><a class="toc-backref" href="#toc-entry-24" role="doc-backlink"><span class="sectnum">3.4 </span>Matrices</a></h3>
<p>The <span class="docutils literal">matrix</span> and <span class="docutils literal">cases</span> environments can also contain <span class="docutils literal">\\</span> and
<span class="docutils literal">&amp;</span>:</p>
<pre class="literal-block">.. math::
   \left ( \begin{matrix} a &amp; b \\ c &amp; d \end{matrix}\right)</pre>
<p>Result:</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <mo stretchy="true">(</mo>
  <mrow>
    <mstyle scriptlevel="0">
      <mtable>
        <mtr>
          <mtd>
            <mi>a</mi>
          </mtd>
          <mtd>
            <mi>b</mi>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mi>c</mi>
          </mtd>
          <mtd>
            <mi>d</mi>
          </mtd>
        </mtr>
      </mtable>
    </mstyle>
  </mrow>
  <mo stretchy="true">)</mo>
</mrow>
</math>
</div>
<p>The environments <span class="docutils literal">pmatrix</span>, <span class="docutils literal">bmatrix</span>, <span class="docutils literal">Bmatrix</span>, <span class="docutils literal">vmatrix</span>, and
<span class="docutils literal">Vmatrix</span> have (respectively) ( ), [ ], { }, | |, and <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo rspace="0.333em">∥</mo>
  <mo lspace="0">∥</mo>
</mrow>
</math>
delimiters built in, e.g.</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <mrow>
    <mo stretchy="true">(</mo>
    <mrow>
      <mstyle scriptlevel="0">
        <mtable>
          <mtr>
            <mtd>
              <mi>a</mi>
            </mtd>
            <mtd>
              <mi>b</mi>
            </mtd>
          </mtr>
          <mtr>
            <mtd>
              <mi>c</mi>
            </mtd>
            <mtd>
              <mi>d</mi>
            </mtd>
          </mtr>
        </mtable>
      </mstyle>
    </mrow>
    <mo stretchy="true">)</mo>
  </mrow>
  <mspace width="2.167em"/>
  <mrow>
    <mo stretchy="true">[</mo>
    <mrow>
      <mstyle scriptlevel="0">
        <mtable>
          <mtr>
            <mtd>
              <mi>a</mi>
            </mtd>
            <mtd>
              <mi>b</mi>
            </mtd>
          </mtr>
          <mtr>
            <mtd>
              <mi>c</mi>
            </mtd>
            <mtd>
              <mi>d</mi>
            </mtd>
          </mtr>
        </mtable>
      </mstyle>
    </mrow>
    <mo stretchy="true">]</mo>
  </mrow>
  <mspace width="2.167em"/>
  <mrow>
    <mo stretchy="true">∥</mo>
    <mrow>
      <mstyle scriptlevel="0">
        <mtable>
          <mtr>
            <mtd>
              <mi>a</mi>
            </mtd>
            <mtd>
              <mi>b</mi>
            </mtd>
          </mtr>
          <mtr>
            <mtd>
              <mi>c</mi>
            </mtd>
            <mtd>
              <mi>d</mi>
            </mtd>
          </mtr>
        </mtable>
      </mstyle>
    </mrow>
    <mo stretchy="true">∥</mo>
  </mrow>
</mrow>
</math>
</div>
<p>To produce a small matrix suitable for use in text, there is a
<span class="docutils literal">smallmatrix</span> environment
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="true" minsize="1.2em" maxsize="1.2em">(</mo>
  <mstyle scriptlevel="1">
    <mstyle scriptlevel="1">
      <mtable>
        <mtr>
          <mtd>
            <mi>a</mi>
          </mtd>
          <mtd>
            <mi>b</mi>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mi>c</mi>
          </mtd>
          <mtd>
            <mi>d</mi>
          </mtd>
        </mtr>
      </mtable>
    </mstyle>
    <mstyle scriptlevel="0">
      <mo stretchy="true" minsize="1.2em" maxsize="1.2em">)</mo>
    </mstyle>
  </mstyle>
</mrow>
</math>
that comes closer to fitting within a single text line than a normal
matrix.</p>
<p>For piecewise function definitions there is a <span class="docutils literal">cases</span> environment:</p>
<pre class="math problematic m">
\mathrm{sgn}(x) = \begin{cases}
            -1 &amp; x&lt;0\\
  \phantom{-}1 &amp; x&gt;0
\end{cases}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 688)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\phantom&quot;</p>
</aside>
</section>
<section id="spacing-commands">
<h3><a class="toc-backref" href="#toc-entry-25" role="doc-backlink"><span class="sectnum">3.5 </span>Spacing commands</a></h3>
<p>Horizontal spacing of elements can be controlled with the following
commands:</p>
<table>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mn>3</mn>
  <mspace width="2.000em"/>
  <mn>4</mn>
</mrow>
</math></p></td>
<td></td>
<td><p><span class="docutils literal">3\qquad 4</span></p></td>
<td><p>= 2em</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mn>3</mn>
  <mspace width="1.000em"/>
  <mn>4</mn>
</mrow>
</math></p></td>
<td></td>
<td><p><span class="docutils literal">3\quad 4</span></p></td>
<td><p>= 1em</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mn>3</mn>
  <mspace width="0.333em"/>
  <mn>4</mn>
</mrow>
</math></p></td>
<td><p><span class="docutils literal">3~4</span></p></td>
<td><p><span class="docutils literal">3\nobreakspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mn>3</mn>
  <mspace width="0.333em"/>
  <mn>4</mn>
</mrow>
</math></p></td>
<td><p><span class="docutils literal">3\ 4</span></p></td>
<td></td>
<td><p>escaped space</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mn>3</mn>
  <mspace width="0.278em"/>
  <mn>4</mn>
</mrow>
</math></p></td>
<td><p><span class="docutils literal"><span class="pre">3\;4</span></span></p></td>
<td><p><span class="docutils literal">3\thickspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><span class="math problematic m">3\:4</span></p></td>
<td><p><span class="docutils literal"><span class="pre">3\:4</span></span></p></td>
<td><p><span class="docutils literal">3\medspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mn>3</mn>
  <mspace width="0.167em"/>
  <mn>4</mn>
</mrow>
</math></p></td>
<td><p><span class="docutils literal"><span class="pre">3\,4</span></span></p></td>
<td><p><span class="docutils literal">3\thinspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mn>34</mn>
</math></p></td>
<td><p><span class="docutils literal">3  4</span></p></td>
<td></td>
<td><p>regular space <a class="brackets" href="#footnote-2" id="footnote-reference-6" role="doc-noteref"><span class="fn-bracket">[</span>4<span class="fn-bracket">]</span></a></p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mn>3</mn>
  <mspace width="-0.167em"/>
  <mn>4</mn>
</mrow>
</math></p></td>
<td><p><span class="docutils literal"><span class="pre">3\!4</span></span></p></td>
<td><p><span class="docutils literal">3\negthinspace 4</span></p></td>
<td><p>negative space <a class="brackets" href="#footnote-3" id="footnote-reference-7" role="doc-noteref"><span class="fn-bracket">[</span>5<span class="fn-bracket">]</span></a></p></td>
</tr>
<tr><td><p><span class="math problematic m">3\negmedspace 4</span></p></td>
<td></td>
<td><p><span class="docutils literal">3\negmedspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><span class="math problematic m">3\negthickspace 4</span></p></td>
<td></td>
<td><p><span class="docutils literal">3\negthickspace 4</span></p></td>
<td></td>
</tr>
<tr><td><p><span class="math problematic m">3\hspace{1ex}4</span></p></td>
<td></td>
<td><p><span class="docutils literal">3\hspace{1ex}4</span></p></td>
<td><p>custom length</p></td>
</tr>
<tr><td><p><span class="math problematic m">3\mspace{20mu}4</span></p></td>
<td></td>
<td><p><span class="docutils literal">3\mspace{20mu}4</span></p></td>
<td><p>custom length <a class="brackets" href="#footnote-4" id="footnote-reference-8" role="doc-noteref"><span class="fn-bracket">[</span>6<span class="fn-bracket">]</span></a></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 708)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\:&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 712)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\negmedspace&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 713)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\negthickspace&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 714)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\hspace&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 715)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\mspace&quot;</p>
</aside>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="footnote-2" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-6">4</a><span class="fn-bracket">]</span></span>
<p>Whitespace characters are ignored in LaTeX math mode.</p>
</aside>
<aside class="footnote brackets" id="footnote-3" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-7">5</a><span class="fn-bracket">]</span></span>
<p>Negative spacing does not work with MathML (last tested in Firefox 115).</p>
</aside>
<aside class="footnote brackets" id="footnote-4" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-8">6</a><span class="fn-bracket">]</span></span>
<p>In LaTeX, the unit must be 'mu' (1 mu = 1/18em).</p>
</aside>
</aside>
<p>There are also three commands that leave a space equal to the height and
width of its argument. For example <span class="docutils literal">\phantom{XXX}</span> results in space as
wide and high as three X’s:</p>
<pre class="math problematic m">
\frac{\phantom{XXX}+1}{XXX-1}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 726)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\phantom&quot;</p>
</aside>
<p>The commands <span class="docutils literal">\hphantom</span> and <span class="docutils literal">\vphantom</span> insert space with the
width or height of the argument. They are not supported with <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a>
MathML.</p>
</section>
<section id="modular-arithmetic-and-modulo-operation">
<h3><a class="toc-backref" href="#toc-entry-26" role="doc-backlink"><span class="sectnum">3.6 </span>Modular arithmetic and modulo operation</a></h3>
<p>The commands <span class="docutils literal">\bmod</span>, <span class="docutils literal">\pmod</span>, <span class="docutils literal">\mod</span>, and <span class="docutils literal">\pod</span> deal with the
special spacing conventions of the “mod” notation. <a class="brackets" href="#footnote-5" id="footnote-reference-9" role="doc-noteref"><span class="fn-bracket">[</span>7<span class="fn-bracket">]</span></a></p>
<table>
<thead>
<tr><th class="head"><p>command</p></th>
<th class="head"><p>example</p></th>
<th class="head"><p>result</p></th>
</tr>
</thead>
<tbody>
<tr><td><p><span class="docutils literal">\bmod</span></p></td>
<td><p><span class="docutils literal">\gcd(n,m \bmod n)</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo>gcd</mo>
  <mo stretchy="false">(</mo>
  <mi>n</mi>
  <mo>,</mo>
  <mi>m</mi>
  <mo lspace="0.278em" rspace="0.278em">mod</mo>
  <mi>n</mi>
  <mo stretchy="false">)</mo>
</mrow>
</math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\pmod</span></p></td>
<td><p><span class="docutils literal">x\equiv y \pmod b</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi>x</mi>
  <mo>≡</mo>
  <mi>y</mi>
  <mo lspace="1.000em" stretchy="false">(</mo>
  <mo rspace="0.333em">mod</mo>
  <mi>b</mi>
  <mo stretchy="false">)</mo>
</mrow>
</math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\mod</span></p></td>
<td><p><span class="docutils literal">x\equiv y \mod c</span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi>x</mi>
  <mo>≡</mo>
  <mi>y</mi>
  <mo lspace="1.000em" rspace="0.333em">mod</mo>
  <mi>c</mi>
</mrow>
</math></p></td>
</tr>
<tr><td><p><span class="docutils literal">\pod</span></p></td>
<td><p><span class="docutils literal">x\equiv y \pod d</span></p></td>
<td><p><span class="math problematic m">x\equiv y \pod d</span></p></td>
</tr>
<tr><td><!--  -->
</td>
<td><p><span class="docutils literal"><span class="pre">\operatorname{mod}(m,n)</span></span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi>mod</mi>
  <mo stretchy="false">(</mo>
  <mi>m</mi>
  <mo>,</mo>
  <mi>n</mi>
  <mo stretchy="false">)</mo>
</mrow>
</math></p></td>
</tr>
</tbody>
</table>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 747)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\pod&quot;</p>
</aside>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="footnote-5" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-9">7</a><span class="fn-bracket">]</span></span>
<p>Currently <a class="reference external" href="https://sourceforge.net/p/docutils/feature-requests/93/">not supported</a> by the &quot;HTML&quot; <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a> option
of the HTML writer.</p>
</aside>
</aside>
</section>
<section id="roots">
<h3><a class="toc-backref" href="#toc-entry-27" role="doc-backlink"><span class="sectnum">3.7 </span>Roots</a></h3>
<table>
<thead>
<tr><th class="head"><p>command</p></th>
<th class="head"><p>example</p></th>
<th class="head"><p>result</p></th>
</tr>
</thead>
<tbody>
<tr><td><p><span class="docutils literal">\sqrt</span></p></td>
<td><p><span class="docutils literal"><span class="pre">\sqrt{x^2-1}</span></span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msqrt>
  <msup>
    <mi>x</mi>
    <mn>2</mn>
  </msup>
  <mo>-</mo>
  <mn>1</mn>
</msqrt>
</math></p></td>
</tr>
<tr><td><!--  -->
</td>
<td><p><span class="docutils literal"><span class="pre">\sqrt[3n]{x^2-1}</span></span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mroot>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
    <mo>-</mo>
    <mn>1</mn>
  </mrow>
  <mrow>
    <mn>3</mn>
    <mi>n</mi>
  </mrow>
</mroot>
</math></p></td>
</tr>
<tr><td><!--  -->
</td>
<td><p><span class="docutils literal"><span class="pre">\sqrt\frac{1}{2}</span></span></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msqrt>
  <mfrac>
    <mn>1</mn>
    <mn>2</mn>
  </mfrac>
</msqrt>
</math></p></td>
</tr>
</tbody>
</table>
</section>
<section id="boxed-formulas">
<h3><a class="toc-backref" href="#toc-entry-28" role="doc-backlink"><span class="sectnum">3.8 </span>Boxed formulas</a></h3>
<p>The command <span class="docutils literal">\boxed</span> puts a box around its argument:</p>
<pre class="math problematic m">
\boxed{\eta \leq C(\delta(\eta) +\Lambda_M(0,\delta))}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 776)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\boxed&quot;</p>
</aside>
</section>
</section>
<section id="fractions-and-related-constructions">
<h2><a class="toc-backref" href="#toc-entry-29" role="doc-backlink"><span class="sectnum">4 </span>Fractions and related constructions</a></h2>
<p>The <span class="docutils literal">\frac</span> command takes two ar guments, numerator and denominator,
and typesets them in normal fraction form. For example, <span class="docutils literal">U = <span class="pre">\frac{R}{I}</span></span>
produces <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mi>U</mi>
  <mo>=</mo>
  <mfrac>
    <mi>R</mi>
    <mi>I</mi>
  </mfrac>
</mrow>
</math>. Use <span class="docutils literal">\dfrac</span> or <span class="docutils literal">\tfrac</span> to
force text style and display style respectively.</p>
<pre class="math problematic m">
\frac{x+1}{x-1}  \quad
\dfrac{x+1}{x-1} \quad
\tfrac{x+1}{x-1}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 787)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\dfrac&quot;</p>
</aside>
<p>and in text: <math xmlns="http://www.w3.org/1998/Math/MathML">
<mfrac>
  <mrow>
    <mi>x</mi>
    <mo>+</mo>
    <mn>1</mn>
  </mrow>
  <mrow>
    <mi>x</mi>
    <mo>-</mo>
    <mn>1</mn>
  </mrow>
</mfrac>
</math>, <span class="math problematic m">\dfrac{x+1}{x-1}</span>, <span class="math problematic m">\tfrac{x+1}{x-1}</span>.</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 791)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\dfrac&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 791)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\tfrac&quot;</p>
</aside>
<p>For binomial expressions such as <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="true">(</mo>
  <mrow>
    <mfrac linethickness="0">
      <mi>n</mi>
      <mi>k</mi>
    </mfrac>
  </mrow>
  <mo stretchy="true">)</mo>
</mrow>
</math>,
there are <span class="docutils literal">\binom</span>, <span class="docutils literal">\dbinom</span> and <span class="docutils literal">\tbinom</span> commands:</p>
<pre class="literal-block">2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}</pre>
<p>prints</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <msup>
    <mn>2</mn>
    <mi>k</mi>
  </msup>
  <mo>-</mo>
  <mrow>
    <mo stretchy="true">(</mo>
    <mrow>
      <mfrac linethickness="0">
        <mi>k</mi>
        <mn>1</mn>
      </mfrac>
    </mrow>
    <mo stretchy="true">)</mo>
  </mrow>
  <mspace width="0.167em"/>
  <msup>
    <mn>2</mn>
    <mrow>
      <mi>k</mi>
      <mo>-</mo>
      <mn>1</mn>
    </mrow>
  </msup>
  <mo>+</mo>
  <mrow>
    <mo stretchy="true">(</mo>
    <mrow>
      <mfrac linethickness="0">
        <mi>k</mi>
        <mn>2</mn>
      </mfrac>
    </mrow>
    <mo stretchy="true">)</mo>
  </mrow>
  <mspace width="0.167em"/>
  <msup>
    <mn>2</mn>
    <mrow>
      <mi>k</mi>
      <mo>-</mo>
      <mn>2</mn>
    </mrow>
  </msup>
</mrow>
</math>
</div>
<p>The <span class="docutils literal">\cfrac</span> command for continued fractions uses displaystyle and
padding for sub-fractions:</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <mfrac>
    <mi>π</mi>
    <mn>4</mn>
  </mfrac>
  <mo>=</mo>
  <mn>1</mn>
  <mo>+</mo>
  <mstyle displaystyle="true">
    <mfrac>
      <msup>
        <mn>1</mn>
        <mn>2</mn>
      </msup>
      <mrow>
        <mn>2</mn>
        <mo>+</mo>
        <mstyle displaystyle="true">
          <mfrac>
            <msup>
              <mn>3</mn>
              <mn>2</mn>
            </msup>
            <mrow>
              <mn>2</mn>
              <mo>+</mo>
              <mstyle displaystyle="true">
                <mfrac>
                  <msup>
                    <mn>5</mn>
                    <mn>2</mn>
                  </msup>
                  <mrow>
                    <mn>2</mn>
                    <mo>+</mo>
                    <mstyle displaystyle="true">
                      <mfrac>
                        <msup>
                          <mn>7</mn>
                          <mn>2</mn>
                        </msup>
                        <mrow>
                          <mn>2</mn>
                          <mo>+</mo>
                          <mo>⋯</mo>
                        </mrow>
                      </mfrac>
                    </mstyle>
                  </mrow>
                </mfrac>
              </mstyle>
            </mrow>
          </mfrac>
        </mstyle>
      </mrow>
    </mfrac>
    <mstyle displaystyle="false">
      <mspace width="2.000em"/>
      <mtext>vs.</mtext>
      <mspace width="2.000em"/>
      <mfrac>
        <mi>π</mi>
        <mn>4</mn>
      </mfrac>
      <mo>=</mo>
      <mn>1</mn>
      <mo>+</mo>
      <mfrac>
        <msup>
          <mn>1</mn>
          <mn>2</mn>
        </msup>
        <mrow>
          <mn>2</mn>
          <mo>+</mo>
          <mfrac>
            <msup>
              <mn>3</mn>
              <mstyle scriptlevel="2">
                <mn>2</mn>
              </mstyle>
            </msup>
            <mrow>
              <mn>2</mn>
              <mo>+</mo>
              <mfrac>
                <mstyle scriptlevel="2">
                  <msup>
                    <mn>5</mn>
                    <mstyle scriptlevel="2">
                      <mn>2</mn>
                    </mstyle>
                  </msup>
                </mstyle>
                <mstyle scriptlevel="2">
                  <mn>2</mn>
                  <mo>+</mo>
                  <mfrac>
                    <mstyle scriptlevel="2">
                      <msup>
                        <mn>7</mn>
                        <mstyle scriptlevel="2">
                          <mn>2</mn>
                        </mstyle>
                      </msup>
                    </mstyle>
                    <mstyle scriptlevel="2">
                      <mn>2</mn>
                      <mo>+</mo>
                      <mo>⋯</mo>
                    </mstyle>
                  </mfrac>
                </mstyle>
              </mfrac>
            </mrow>
          </mfrac>
        </mrow>
      </mfrac>
    </mstyle>
  </mstyle>
</mrow>
</math>
</div>
<p>The optional argument <span class="docutils literal">[l]</span> or <span class="docutils literal">[r]</span> for left or right placement of
the numerator is <a class="reference external" href="https://github.com/w3c/mathml/issues/30">not supported by MathML Core</a>:</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mstyle displaystyle="true">
  <mfrac>
    <mo stretchy="false">[</mo>
    <mi>l</mi>
  </mfrac>
  <mstyle displaystyle="false">
    <mo stretchy="false">]</mo>
    <mi>x</mi>
    <mi>x</mi>
    <mo>-</mo>
    <mn>1</mn>
    <mstyle displaystyle="true">
      <mspace width="1.000em"/>
      <mfrac>
        <mi>x</mi>
        <mrow>
          <mi>x</mi>
          <mo>-</mo>
          <mn>1</mn>
        </mrow>
      </mfrac>
      <mspace width="1.000em"/>
      <mfrac>
        <mo stretchy="false">[</mo>
        <mi>r</mi>
      </mfrac>
      <mstyle displaystyle="false">
        <mo stretchy="false">]</mo>
        <mi>x</mi>
        <mi>x</mi>
        <mo>-</mo>
        <mn>1</mn>
      </mstyle>
    </mstyle>
  </mstyle>
</mstyle>
</math>
</div>
</section>
<section id="delimiter-sizes">
<h2><a class="toc-backref" href="#toc-entry-30" role="doc-backlink"><span class="sectnum">5 </span>Delimiter sizes</a></h2>
<p>Besides the automatic scaling of <a class="reference internal" href="#extensible-delimiters">extensible delimiters</a> with <span class="docutils literal">\left</span>
and <span class="docutils literal">\right</span>, there are four commands to manually select delimiters of
fixed size:</p>
<table>
<tbody>
<tr><td><p>Sizing</p></td>
<td><p>no</p></td>
<td><p><span class="docutils literal">\left</span></p></td>
<td><p><span class="docutils literal">\bigl</span></p></td>
<td><p><span class="docutils literal">\Bigl</span></p></td>
<td><p><span class="docutils literal">\biggl</span></p></td>
<td><p><span class="docutils literal">\Biggl</span></p></td>
</tr>
<tr><td><p>command</p></td>
<td></td>
<td><p><span class="docutils literal">\right</span></p></td>
<td><p><span class="docutils literal">\bigr</span></p></td>
<td><p><span class="docutils literal">\Bigr</span></p></td>
<td><p><span class="docutils literal">\biggr</span></p></td>
<td><p><span class="docutils literal">\Biggr</span></p></td>
</tr>
<tr><td><p>Result</p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle displaystyle="true">
  <mo stretchy="false">(</mo>
  <mi>b</mi>
  <mo stretchy="false">)</mo>
  <mo stretchy="false">(</mo>
  <mfrac>
    <mi>c</mi>
    <mi>d</mi>
  </mfrac>
  <mo stretchy="false">)</mo>
</mstyle>
</math></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle displaystyle="true">
  <mrow>
    <mo stretchy="true">(</mo>
    <mrow>
      <mi>b</mi>
    </mrow>
    <mo stretchy="true">)</mo>
  </mrow>
  <mspace width="0.167em"/>
  <mrow>
    <mo stretchy="true">(</mo>
    <mrow>
      <mfrac>
        <mi>c</mi>
        <mi>d</mi>
      </mfrac>
    </mrow>
    <mo stretchy="true">)</mo>
  </mrow>
</mstyle>
</math></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle displaystyle="true">
  <mo stretchy="true" minsize="1.2em" maxsize="1.2em">(</mo>
  <mi>b</mi>
  <mo stretchy="true" minsize="1.2em" maxsize="1.2em">)</mo>
  <mo stretchy="true" minsize="1.2em" maxsize="1.2em">(</mo>
  <mfrac>
    <mi>c</mi>
    <mi>d</mi>
  </mfrac>
  <mo stretchy="true" minsize="1.2em" maxsize="1.2em">)</mo>
</mstyle>
</math></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle displaystyle="true">
  <mo stretchy="true" minsize="1.8em" maxsize="1.8em">(</mo>
  <mi>b</mi>
  <mo stretchy="true" minsize="1.8em" maxsize="1.8em">)</mo>
  <mo stretchy="true" minsize="1.8em" maxsize="1.8em">(</mo>
  <mfrac>
    <mi>c</mi>
    <mi>d</mi>
  </mfrac>
  <mo stretchy="true" minsize="1.8em" maxsize="1.8em">)</mo>
</mstyle>
</math></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle displaystyle="true">
  <mo stretchy="true" minsize="2.4em" maxsize="2.4em">(</mo>
  <mi>b</mi>
  <mo stretchy="true" minsize="2.4em" maxsize="2.4em">)</mo>
  <mo stretchy="true" minsize="2.4em" maxsize="2.4em">(</mo>
  <mfrac>
    <mi>c</mi>
    <mi>d</mi>
  </mfrac>
  <mo stretchy="true" minsize="2.4em" maxsize="2.4em">)</mo>
</mstyle>
</math></p></td>
<td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle displaystyle="true">
  <mo stretchy="true" minsize="3em" maxsize="3em">(</mo>
  <mi>b</mi>
  <mo stretchy="true" minsize="3em" maxsize="3em">)</mo>
  <mo stretchy="true" minsize="3em" maxsize="3em">(</mo>
  <mfrac>
    <mi>c</mi>
    <mi>d</mi>
  </mfrac>
  <mo stretchy="true" minsize="3em" maxsize="3em">)</mo>
</mstyle>
</math></p></td>
</tr>
</tbody>
</table>
<p>There are two or three situations where the delimiter size is commonly
adjusted using these commands:</p>
<p>The first kind of adjustment is done for cumulative operators with
limits, such as summation signs. With <span class="docutils literal">\left</span> and <span class="docutils literal">\right</span> the
delimiters usually turn out larger than necessary, and using the <span class="docutils literal">Big</span>
or <span class="docutils literal">bigg</span> sizes instead gives better results:</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <msup>
    <mrow>
      <mo stretchy="true">[</mo>
      <mrow>
        <msub>
          <mo stretchy="false">∑</mo>
          <mi>i</mi>
        </msub>
        <msub>
          <mi>a</mi>
          <mi>i</mi>
        </msub>
        <mspace width="0.167em"/>
        <msup>
          <mrow>
            <mo stretchy="true">|</mo>
            <mrow>
              <msub>
                <mo stretchy="false">∑</mo>
                <mi>j</mi>
              </msub>
              <msub>
                <mi>x</mi>
                <mrow>
                  <mi>i</mi>
                  <mi>j</mi>
                </mrow>
              </msub>
            </mrow>
            <mo stretchy="true">|</mo>
          </mrow>
          <mi>p</mi>
        </msup>
      </mrow>
      <mo stretchy="true">]</mo>
    </mrow>
    <mrow>
      <mn>1</mn>
      <mo stretchy="false">/</mo>
      <mi>p</mi>
    </mrow>
  </msup>
  <mspace width="0.167em"/>
  <mtext> versus </mtext>
  <mo stretchy="true" minsize="2.4em" maxsize="2.4em">[</mo>
  <msub>
    <mo stretchy="false">∑</mo>
    <mi>i</mi>
  </msub>
  <msub>
    <mi>a</mi>
    <mi>i</mi>
  </msub>
  <mo stretchy="true" minsize="1.8em" maxsize="1.8em">|</mo>
  <msub>
    <mo stretchy="false">∑</mo>
    <mi>j</mi>
  </msub>
  <msub>
    <mi>x</mi>
    <mrow>
      <mi>i</mi>
      <mi>j</mi>
    </mrow>
  </msub>
  <msup>
    <mo stretchy="true" minsize="1.8em" maxsize="1.8em">|</mo>
    <mi>p</mi>
  </msup>
  <msup>
    <mo stretchy="true" minsize="2.4em" maxsize="2.4em">]</mo>
    <mrow>
      <mn>1</mn>
      <mo stretchy="false">/</mo>
      <mi>p</mi>
    </mrow>
  </msup>
</mrow>
</math>
</div>
<p>The second kind of situation is clustered pairs of delimiters, where
left and right make them all the same size (because that is adequate to
cover the encompassed material), but what you really want is to make some
of the delimiters slightly larger to make the nesting easier to see.</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <mrow>
    <mo stretchy="true">(</mo>
    <mrow>
      <mo stretchy="false">(</mo>
      <msub>
        <mi>a</mi>
        <mn>1</mn>
      </msub>
      <msub>
        <mi>b</mi>
        <mn>1</mn>
      </msub>
      <mo stretchy="false">)</mo>
      <mo>-</mo>
      <mo stretchy="false">(</mo>
      <msub>
        <mi>a</mi>
        <mn>2</mn>
      </msub>
      <msub>
        <mi>b</mi>
        <mn>2</mn>
      </msub>
      <mo stretchy="false">)</mo>
    </mrow>
    <mo stretchy="true">)</mo>
  </mrow>
  <mspace width="0.167em"/>
  <mrow>
    <mo stretchy="true">(</mo>
    <mrow>
      <mo stretchy="false">(</mo>
      <msub>
        <mi>a</mi>
        <mn>2</mn>
      </msub>
      <msub>
        <mi>b</mi>
        <mn>1</mn>
      </msub>
      <mo stretchy="false">)</mo>
      <mo>+</mo>
      <mo stretchy="false">(</mo>
      <msub>
        <mi>a</mi>
        <mn>1</mn>
      </msub>
      <msub>
        <mi>b</mi>
        <mn>2</mn>
      </msub>
      <mo stretchy="false">)</mo>
    </mrow>
    <mo stretchy="true">)</mo>
  </mrow>
  <mspace width="1.167em"/>
  <mtext>versus</mtext>
  <mo lspace="1.000em" stretchy="true" minsize="1.2em" maxsize="1.2em">(</mo>
  <mo stretchy="false">(</mo>
  <msub>
    <mi>a</mi>
    <mn>1</mn>
  </msub>
  <msub>
    <mi>b</mi>
    <mn>1</mn>
  </msub>
  <mo stretchy="false">)</mo>
  <mo>-</mo>
  <mo stretchy="false">(</mo>
  <msub>
    <mi>a</mi>
    <mn>2</mn>
  </msub>
  <msub>
    <mi>b</mi>
    <mn>2</mn>
  </msub>
  <mo stretchy="false">)</mo>
  <mo stretchy="true" minsize="1.2em" maxsize="1.2em">)</mo>
  <mo stretchy="true" minsize="1.2em" maxsize="1.2em">(</mo>
  <mo stretchy="false">(</mo>
  <msub>
    <mi>a</mi>
    <mn>2</mn>
  </msub>
  <msub>
    <mi>b</mi>
    <mn>1</mn>
  </msub>
  <mo stretchy="false">)</mo>
  <mo>+</mo>
  <mo stretchy="false">(</mo>
  <msub>
    <mi>a</mi>
    <mn>1</mn>
  </msub>
  <msub>
    <mi>b</mi>
    <mn>2</mn>
  </msub>
  <mo stretchy="false">)</mo>
  <mo stretchy="true" minsize="1.2em" maxsize="1.2em">)</mo>
</mrow>
</math>
</div>
<p>The third kind of situation is a slightly oversize object in running
text, such as <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="true">|</mo>
  <mrow>
    <mfrac>
      <msup>
        <mi>b</mi>
        <mo>′</mo>
      </msup>
      <msup>
        <mi>d</mi>
        <mo>′</mo>
      </msup>
    </mfrac>
  </mrow>
  <mo stretchy="true">|</mo>
</mrow>
</math> where the delimiters produced
by <span class="docutils literal">\left</span> and <span class="docutils literal">\right</span> cause too much line spreading. <a class="brackets" href="#footnote-6" id="footnote-reference-10" role="doc-noteref"><span class="fn-bracket">[</span>8<span class="fn-bracket">]</span></a> In that case
<span class="docutils literal">\bigl</span> and <span class="docutils literal">\bigr</span> can be used to produce delimiters that are larger
than the base size but still able to fit within the normal line spacing:
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="true" minsize="1.2em" maxsize="1.2em">|</mo>
  <mfrac>
    <msup>
      <mi>b</mi>
      <mo>′</mo>
    </msup>
    <msup>
      <mi>d</mi>
      <mo>′</mo>
    </msup>
  </mfrac>
  <mo stretchy="true" minsize="1.2em" maxsize="1.2em">|</mo>
</mrow>
</math>.</p>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="footnote-6" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-10">8</a><span class="fn-bracket">]</span></span>
<p>With MathML, an example would be parentheses
around a <span class="docutils literal">smallmatrix</span> environment
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="true">(</mo>
  <mrow>
    <mstyle scriptlevel="1">
      <mtable>
        <mtr>
          <mtd>
            <mi>a</mi>
          </mtd>
          <mtd>
            <mi>b</mi>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mi>c</mi>
          </mtd>
          <mtd>
            <mi>d</mi>
          </mtd>
        </mtr>
      </mtable>
    </mstyle>
  </mrow>
  <mo stretchy="true">)</mo>
</mrow>
</math>
vs. <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mo stretchy="true" minsize="1.8em" maxsize="1.8em">(</mo>
  <mstyle scriptlevel="1">
    <mstyle scriptlevel="1">
      <mtable>
        <mtr>
          <mtd>
            <mi>a</mi>
          </mtd>
          <mtd>
            <mi>b</mi>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mi>c</mi>
          </mtd>
          <mtd>
            <mi>d</mi>
          </mtd>
        </mtr>
      </mtable>
    </mstyle>
    <mstyle scriptlevel="0">
      <mo stretchy="true" minsize="1.8em" maxsize="1.8em">)</mo>
    </mstyle>
  </mstyle>
</mrow>
</math>.</p>
</aside>
</aside>
</section>
<section id="text">
<h2><a class="toc-backref" href="#toc-entry-31" role="doc-backlink"><span class="sectnum">6 </span>Text</a></h2>
<p>The main use of the command <span class="docutils literal">\text</span> is for words or phrases in a
display. It is similar to <span class="docutils literal">\mbox</span> in its effects but, unlike <span class="docutils literal">\mbox</span>,
automatically produces subscript-size text if used in a subscript,
<span class="docutils literal"><span class="pre">k_{\text{B}}T</span></span> becomes <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <msub>
    <mi>k</mi>
    <mtext>B</mtext>
  </msub>
  <mi>T</mi>
</mrow>
</math>.</p>
<p>Whitespace is kept inside the argument:</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <msub>
    <mi>f</mi>
    <mrow>
      <mo stretchy="false">[</mo>
      <msub>
        <mi>x</mi>
        <mrow>
          <mi>i</mi>
          <mo>-</mo>
          <mn>1</mn>
        </mrow>
      </msub>
      <mo>,</mo>
      <msub>
        <mi>x</mi>
        <mi>i</mi>
      </msub>
      <mo stretchy="false">]</mo>
    </mrow>
  </msub>
  <mtext> is monotonic for </mtext>
  <mi>i</mi>
  <mo>=</mo>
  <mn>1</mn>
  <mo rspace="0.333em">,</mo>
  <mo lspace="0">…</mo>
  <mo rspace="0.333em">,</mo>
  <mi>c</mi>
  <mo>+</mo>
  <mn>1</mn>
</mrow>
</math>
</div>
<p>The text may contain math commands wrapped in <span class="docutils literal">$</span> signs, e.g.</p>
<pre class="math problematic m">
(-1)^{n_i} = \begin{cases} -1 \quad \text{if $n_i$ is odd,} \\
              +1 \quad \text{if $n_i$ is even.}
\end{cases}
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 898)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">The command &quot;$&quot; is illegal in text mode (perhaps you intended to use &quot;\$&quot; instead?)</p>
</aside>
<!-- TODO ignore {}, handle text-mode commands -->
</section>
<section id="integrals-and-sums">
<h2><a class="toc-backref" href="#toc-entry-32" role="doc-backlink"><span class="sectnum">7 </span>Integrals and sums</a></h2>
<p>The limits on integrals, sums, and similar symbols are placed either to
the side of or above and below the base symbol, depending on convention
and context. In inline formulas and fractions, the limits on sums, and
similar symbols like</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <msub>
    <mo>lim</mo>
    <mrow>
      <mi>n</mi>
      <mo>→</mo>
      <mi mathvariant="normal">∞</mi>
    </mrow>
  </msub>
  <msubsup>
    <mo stretchy="false">∑</mo>
    <mn>1</mn>
    <mi>n</mi>
  </msubsup>
  <mfrac>
    <mn>1</mn>
    <mi>n</mi>
  </mfrac>
</mrow>
</math>
</div>
<p>move to index positions: <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <msub>
    <mo>lim</mo>
    <mrow>
      <mi>n</mi>
      <mo>→</mo>
      <mi mathvariant="normal">∞</mi>
    </mrow>
  </msub>
  <msubsup>
    <mo stretchy="false">∑</mo>
    <mn>1</mn>
    <mi>n</mi>
  </msubsup>
  <mfrac>
    <mn>1</mn>
    <mi>n</mi>
  </mfrac>
</mrow>
</math>.</p>
<section id="altering-the-placement-of-limits">
<h3><a class="toc-backref" href="#toc-entry-33" role="doc-backlink"><span class="sectnum">7.1 </span>Altering the placement of limits</a></h3>
<p>The commands <span class="docutils literal">\intop</span> and <span class="docutils literal">\ointop</span> produce integral signs with
limits as in sums and similar: <span class="math problematic m">\intop_0^1</span>, <span class="math problematic m">\ointop_c</span> and</p>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 921)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\intop&quot;</p>
</aside>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 921)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\ointop&quot;</p>
</aside>
<pre class="math problematic m">
\intop_0^1 \quad \ointop_c
   \quad \text{vs.} \quad
\int^1_0   \quad \oint_c
</pre>
<aside class="system-message">
<p class="system-message-title">System Message: WARNING/2 (<span class="docutils literal">/usr/local/src/docutils-git-svn/docutils/docs/ref/rst/mathematics.txt</span>, line 924)</p>
<p>TeX to MathML converter `blahtexml` failed:</p>
<p class="pre-wrap">Unrecognised command &quot;\intop&quot;</p>
</aside>
<p>The commands <span class="docutils literal">\limits</span> and <span class="docutils literal">\nolimits</span> override the default placement
of the limits for any operator; <span class="docutils literal">\displaylimits</span> forces standard
positioning as for the sum command. They should follow immediately after
the operator to which they apply.</p>
<p>Compare the same term with default positions, <span class="docutils literal">\limits</span>, and
<span class="docutils literal">\nolimits</span> in inline and display mode: <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <msub>
    <mo>lim</mo>
    <mrow>
      <mi>x</mi>
      <mo>→</mo>
      <mn>0</mn>
    </mrow>
  </msub>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</mrow>
</math>,
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <munder>
    <mo movablelimits="false">lim</mo>
    <mrow>
      <mi>x</mi>
      <mo>→</mo>
      <mn>0</mn>
    </mrow>
  </munder>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</mrow>
</math>, <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <msub>
    <mo>lim</mo>
    <mrow>
      <mi>x</mi>
      <mo>→</mo>
      <mn>0</mn>
    </mrow>
  </msub>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</mrow>
</math>, vs.</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <msub>
    <mo>lim</mo>
    <mrow>
      <mi>x</mi>
      <mo>→</mo>
      <mn>0</mn>
    </mrow>
  </msub>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo rspace="1.167em">,</mo>
  <munder>
    <mo lspace="0" movablelimits="false">lim</mo>
    <mrow>
      <mi>x</mi>
      <mo>→</mo>
      <mn>0</mn>
    </mrow>
  </munder>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo rspace="1.167em" stretchy="false">)</mo>
  <msub>
    <mo lspace="0">lim</mo>
    <mrow>
      <mi>x</mi>
      <mo>→</mo>
      <mn>0</mn>
    </mrow>
  </msub>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>.</mo>
</mrow>
</math>
</div>
<!-- TODO: \substack -->
<!-- TODO: \sideset -->
</section>
</section>
<section id="changing-the-size-of-elements-in-a-formula">
<h2><a class="toc-backref" href="#toc-entry-34" role="doc-backlink"><span class="sectnum">8 </span>Changing the size of elements in a formula</a></h2>
<p>The declarations <a class="brackets" href="#footnote-7" id="footnote-reference-11" role="doc-noteref"><span class="fn-bracket">[</span>9<span class="fn-bracket">]</span></a> <span class="docutils literal">\displaystyle</span>, <span class="docutils literal">\textstyle</span>,
<span class="docutils literal">\scriptstyle</span>, and <span class="docutils literal">\scriptscriptstyle</span>, select a symbol size and
spacing that would be applied in display math, inline
math, first-order subscript, or second-order subscript, respectively
even when the current context would normally yield some other size.</p>
<p>For example <span class="docutils literal"><span class="pre">:math:`\displaystyle</span> <span class="pre">\sum_{n=0}^\infty</span> <span class="pre">\frac{1}{n}`</span></span> is printed as <math xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle displaystyle="true">
  <munderover>
    <mo stretchy="false">∑</mo>
    <mrow>
      <mi>n</mi>
      <mo>=</mo>
      <mn>0</mn>
    </mrow>
    <mi mathvariant="normal">∞</mi>
  </munderover>
  <mfrac>
    <mn>1</mn>
    <mi>n</mi>
  </mfrac>
</mstyle>
</math>
rather than <math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <msubsup>
    <mo stretchy="false">∑</mo>
    <mrow>
      <mi>n</mi>
      <mo>=</mo>
      <mn>0</mn>
    </mrow>
    <mi mathvariant="normal">∞</mi>
  </msubsup>
  <mfrac>
    <mn>1</mn>
    <mi>n</mi>
  </mfrac>
</mrow>
</math> and</p>
<pre class="literal-block">\frac{\scriptstyle\sum_{n &gt; 0} z^n}
{\displaystyle\prod_{1\leq k\leq n} (1-q^k)}</pre>
<p>yields</p>
<div>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
  <mfrac>
    <mrow>
      <msub>
        <mo stretchy="false">∑</mo>
        <mrow>
          <mi>n</mi>
          <mo>&gt;</mo>
          <mn>0</mn>
        </mrow>
      </msub>
      <msup>
        <mi>z</mi>
        <mi>n</mi>
      </msup>
    </mrow>
    <mstyle displaystyle="true" scriptlevel="0">
      <munder>
        <mo stretchy="false">∏</mo>
        <mrow>
          <mn>1</mn>
          <mo>≤</mo>
          <mi>k</mi>
          <mo>≤</mo>
          <mi>n</mi>
        </mrow>
      </munder>
      <mo stretchy="false">(</mo>
      <mn>1</mn>
      <mo>-</mo>
      <msup>
        <mi>q</mi>
        <mi>k</mi>
      </msup>
      <mo stretchy="false">)</mo>
    </mstyle>
  </mfrac>
  <mtext> instead of the default </mtext>
  <mfrac>
    <mrow>
      <msub>
        <mo stretchy="false">∑</mo>
        <mrow>
          <mi>n</mi>
          <mo>&gt;</mo>
          <mn>0</mn>
        </mrow>
      </msub>
      <msup>
        <mi>z</mi>
        <mi>n</mi>
      </msup>
    </mrow>
    <mrow>
      <msub>
        <mo stretchy="false">∏</mo>
        <mrow>
          <mn>1</mn>
          <mo>≤</mo>
          <mi>k</mi>
          <mo>≤</mo>
          <mi>n</mi>
        </mrow>
      </msub>
      <mo stretchy="false">(</mo>
      <mn>1</mn>
      <mo>-</mo>
      <msup>
        <mi>q</mi>
        <mi>k</mi>
      </msup>
      <mo stretchy="false">)</mo>
    </mrow>
  </mfrac>
  <mo>.</mo>
</mrow>
</math>
</div>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="footnote-7" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#footnote-reference-11">9</a><span class="fn-bracket">]</span></span>
<p>&quot;Declarations&quot; are commands that affect processing of the current
&quot;group&quot;. In particular, notice where the braces fall that delimit the
effect of the command: Right: <span class="docutils literal">{\displaystyle <span class="pre">...}</span></span> Wrong:
<span class="docutils literal"><span class="pre">\displaystyle{...}</span></span>.</p>
<p>With <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a> MathML, the declaration must be the first element
after the opening bracket.</p>
</aside>
</aside>
<div role="list" class="citation-list">
<div class="citation" id="iso-80000-2" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#citation-reference-1">ISO-80000-2</a><span class="fn-bracket">]</span></span>
<p><cite>Quantities and units – Part 2: Mathematical signs
and symbols to be used in the natural sciences and technology</cite>:
<a class="reference external" href="http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=31887">http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=31887</a>.</p>
</div>
</div>
</section>
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